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im solving 4 ODe with boundary conditions.. i got this error Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 8, got 7


i solve 4 ODE with boundary condition.. i try to plot a graph F(eta) with different value of M.. but it doesnt comeout.. anyone can help me please??

restart; with*plots; n := .2; B := .5; R := 2; N := 10

Eq1 := diff(f(eta), eta, eta, eta)+f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta))) = 0;

diff(diff(diff(f(eta), eta), eta), eta)+f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+.5*H(eta)*(F(eta)-(diff(f(eta), eta))) = 0

(1)

Eq2 := G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0;

G(eta)*(diff(F(eta), eta))+F(eta)^2+.5*F(eta)-.5*(diff(f(eta), eta)) = 0

(2)

Eq3 := G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0;

G(eta)*(diff(G(eta), eta))+.5*f(eta)+.5*G(eta) = 0

(3)

Eq4 := G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0;

G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0

(4)

bcs1 := f(0) = R, (D(f))(0) = 1, (D(f))(N) = 0, F(N) = 0, G(N) = -f(N), H(N) = n;

f(0) = 2, (D(f))(0) = 1, (D(f))(10) = 0, F(10) = 0, G(10) = -f(10), H(10) = .2

(5)

L := [2, 3, 5];

[2, 3, 5]

(6)

for k to 3 do R := dsolve(eval({Eq1, Eq2, Eq3, Eq4, bcs1}, M = L[k]), [f(eta), F(eta), G(eta), H(eta)], numeric, output = listprocedure); Y || k := rhs(R[5]); YP || k := rhs(R[6]); YR || k := rhs(R[7]) end do:

odeplot(R, [eta, f(eta)], 0 .. 10);

odeplot([eta = proc (eta) local _res, _dat, _solnproc; option `Copyright (c) 1993 by the University of Waterloo. All rights reserved.`; _dat := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (4) = 0}); _solnproc := _dat[1]; if member(eta, ["last", 'last']) then _res := _solnproc("last"); if type(_res, 'list') then return _res[1] end if elif type(eta, `=`) and member(lhs(eta), ["initial", 'initial']) then if type(rhs(eta), 'list') then _res := _solnproc("initial" = [0, op(rhs(eta))]) else _res := _solnproc("initial" = [1, rhs(eta)]) end if; if type(_res, 'list') then return _res[1] end if elif eta = "sysvars" then return _dat[3] end if; eta end proc, f(eta) = proc (eta) local res, data, solnproc, `f(eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `f(eta)` := pointto(data[2][2]); return ('`f(eta)`')(eta) end if end if; try res := solnproc(outpoint); res[2] catch: error  end try end proc, diff(f(eta), eta) = proc (eta) local res, data, solnproc, `diff(f(eta),eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `diff(f(eta),eta)` := pointto(data[2][3]); return ('`diff(f(eta),eta)`')(eta) end if end if; try res := solnproc(outpoint); res[3] catch: error  end try end proc, diff(diff(f(eta), eta), eta) = proc (eta) local res, data, solnproc, `diff(diff(f(eta),eta),eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `diff(diff(f(eta),eta),eta)` := pointto(data[2][4]); return ('`diff(diff(f(eta),eta),eta)`')(eta) end if end if; try res := solnproc(outpoint); res[4] catch: error  end try end proc, F(eta) = proc (eta) local res, data, solnproc, `F(eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `F(eta)` := pointto(data[2][5]); return ('`F(eta)`')(eta) end if end if; try res := solnproc(outpoint); res[5] catch: error  end try end proc, G(eta) = proc (eta) local res, data, solnproc, `G(eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `G(eta)` := pointto(data[2][6]); return ('`G(eta)`')(eta) end if end if; try res := solnproc(outpoint); res[6] catch: error  end try end proc, H(eta) = proc (eta) local res, data, solnproc, `H(eta)`, outpoint; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](eta) else outpoint := evalf(eta) end if; data := Array(1..4, {(1) = proc (outpoint) local X, Y, YP, yout, errproc, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = 2.0, (1, 2) = 1.0, (1, 3) = -3.6635195629241393, (1, 4) = 0.5664455547330383e-1, (1, 5) = -2.257448492818163, (1, 6) = .2000045400222303, (2, 1) = 2.1585646422867106, (2, 2) = .4190953434097267, (2, 3) = -1.5353639315426824, (2, 4) = 0.23739324976304817e-1, (2, 5) = -2.266472656603632, (2, 6) = .20000079253347625, (3, 1) = 2.2256794646729534, (3, 2) = .1732188888188128, (3, 3) = -.6345907597520679, (3, 4) = 0.9811836751309456e-2, (3, 5) = -2.2702817767717014, (3, 6) = .20000013503934225, (4, 1) = 2.253701827323839, (4, 2) = 0.7055841966143796e-1, (4, 3) = -.25849213901493645, (4, 4) = 0.3996720985706207e-2, (4, 5) = -2.271870358726635, (4, 6) = .20000002238206496, (5, 1) = 2.2652356250281156, (5, 2) = 0.28304128061312158e-1, (5, 3) = -.10369272213335051, (5, 4) = 0.16032629370674866e-2, (5, 5) = -2.2725238941421693, (5, 6) = .20000000360006479, (6, 1) = 2.26991193450931, (6, 2) = 0.11172377576572433e-1, (6, 3) = -0.4093022194751972e-1, (6, 4) = 0.6328496945703798e-3, (6, 5) = -2.2727888141966752, (6, 6) = .2000000005608222, (7, 1) = 2.27177850048646, (7, 2) = 0.43341769160095515e-2, (7, 3) = -0.158783411959884e-1, (7, 4) = 0.24550571412224227e-3, (7, 5) = -2.2728945496311734, (7, 6) = .20000000008439528, (8, 1) = 2.2725154448203364, (8, 2) = 0.16343670553362268e-2, (8, 3) = -0.5987535406834639e-2, (8, 4) = 0.9257731255239544e-4, (8, 5) = -2.2729362940302473, (8, 6) = .20000000001200044, (9, 1) = 2.272799298891629, (9, 2) = 0.5944621596263174e-3, (9, 3) = -0.2177823651770427e-2, (9, 4) = 0.3367279643313292e-4, (9, 5) = -2.272952372817689, (9, 6) = .2000000000015876, (10, 1) = 2.2729048812302604, (10, 2) = 0.20765921421315688e-3, (10, 3) = -0.7607635589551353e-3, (10, 4) = 0.11762677126566138e-4, (10, 5) = -2.272958353454059, (10, 6) = .20000000000019372, (11, 1) = 2.2729426475725667, (11, 2) = 0.6930148666691294e-4, (11, 3) = -0.2538873405515502e-3, (11, 4) = 0.3925522954238184e-5, (11, 5) = -2.2729604926979117, (11, 6) = .20000000000002158, (12, 1) = 2.272955568683781, (12, 2) = 0.2196474511965646e-4, (12, 3) = -0.8046826976635028e-4, (12, 4) = 0.12441740473087036e-5, (12, 5) = -2.2729612246033346, (12, 6) = .20000000000000212, (13, 1) = 2.272959741660287, (13, 2) = 0.6676964756121347e-5, (13, 3) = -0.24461189888116446e-4, (13, 4) = 0.37821091112128746e-6, (13, 5) = -2.272961460978012, (13, 6) = .20000000000000018, (14, 1) = 2.2729610309665778, (14, 2) = 0.19535661469372987e-5, (14, 3) = -0.7156927469988826e-5, (14, 4) = 0.11065806984458966e-6, (14, 5) = -2.272961534009656, (14, 6) = .20000000000000007, (15, 1) = 2.2729614146384676, (15, 2) = 0.5479767419950037e-6, (15, 3) = -0.20075234226639988e-5, (15, 4) = 0.3103967002724004e-7, (15, 5) = -2.272961555742421, (15, 6) = .2, (16, 1) = 2.272961524178185, (16, 2) = 0.14667586063369783e-6, (16, 3) = -0.537349860305963e-6, (16, 4) = 0.8308327639763628e-8, (16, 5) = -2.272961561947204, (16, 6) = .2, (17, 1) = 2.2729615538420798, (17, 2) = 0.3800160977592546e-7, (17, 3) = -0.13921963448111635e-6, (17, 4) = 0.2152568407973205e-8, (17, 5) = -2.2729615636274887, (17, 6) = .2, (18, 1) = 2.2729615615729086, (18, 2) = 0.9679561461926475e-8, (18, 3) = -0.3546126115859928e-7, (18, 4) = 0.5482904022821568e-9, (18, 5) = -2.2729615640653966, (18, 6) = .2, (19, 1) = 2.2729615635538627, (19, 2) = 0.2422302810354404e-8, (19, 3) = -0.887415332982281e-8, (19, 4) = 0.1372092429861907e-9, (19, 5) = -2.2729615641776046, (19, 6) = .2, (20, 1) = 2.2729615640525562, (20, 2) = 0.5953273783129685e-9, (20, 3) = -0.2180993399969996e-8, (20, 4) = 0.33721794108851795e-10, (20, 5) = -2.2729615642058527, (20, 6) = .2, (21, 1) = 2.2729615641754815, (21, 2) = 0.1449905234394885e-9, (21, 3) = -0.5311755988963094e-9, (21, 4) = 0.8212850309939671e-11, (21, 5) = -2.272961564212815, (21, 6) = .2, (22, 1) = 2.2729615642054646, (22, 2) = 0.35141204232587883e-10, (22, 3) = -0.1287404896150451e-9, (22, 4) = 0.1990529319364229e-11, (22, 5) = -2.272961564214514, (22, 6) = .2, (23, 1) = 2.2729615642127436, (23, 2) = 0.8475375824080267e-11, (23, 3) = -0.31049713824358454e-10, (23, 4) = 0.4800654088689372e-12, (23, 5) = -2.272961564214928, (23, 6) = .2, (24, 1) = 2.2729615642145027, (24, 2) = 0.2035026044727397e-11, (24, 3) = -0.7455373957382428e-11, (24, 4) = 0.1152563122926313e-12, (24, 5) = -2.2729615642150267, (24, 6) = .2, (25, 1) = 2.272961564214925, (25, 2) = 0.4878470512049615e-12, (25, 3) = -0.17872647776069955e-11, (25, 4) = 0.27616758209130112e-13, (25, 5) = -2.2729615642150507, (25, 6) = .2, (26, 1) = 2.272961564215026, (26, 2) = 0.11680457358602633e-12, (26, 3) = -0.4279624747605665e-12, (26, 4) = 0.6598695925952555e-14, (26, 5) = -2.272961564215056, (26, 6) = .2, (27, 1) = 2.2729615642150507, (27, 2) = 0.2792139704425265e-13, (27, 3) = -0.102369938457817e-12, (27, 4) = 0.15638227918490053e-14, (27, 5) = -2.272961564215056, (27, 6) = .2, (28, 1) = 2.272961564215056, (28, 2) = 0.7229355869199076e-14, (28, 3) = -0.26616390820104455e-13, (28, 4) = 0.39247571566227624e-15, (28, 5) = -2.272961564215058, (28, 6) = .2, (29, 1) = 2.272961564215057, (29, 2) = 0.22004123056338692e-14, (29, 3) = -0.8265952539377097e-14, (29, 4) = 0.1094750766735948e-15, (29, 5) = -2.272961564215058, (29, 6) = .2, (30, 1) = 2.272961564215058, (30, 2) = 0.7209052523906788e-15, (30, 3) = -0.2945870798181565e-14, (30, 4) = 0.2889761259240128e-16, (30, 5) = -2.272961564215058, (30, 6) = .2, (31, 1) = 2.272961564215058, (31, 2) = 0.21108792459646215e-15, (31, 3) = -0.12124057648366197e-14, (31, 4) = 0.493978978622271e-17, (31, 5) = -2.272961564215058, (31, 6) = .2, (32, 1) = 2.272961564215058, (32, 2) = -0.34565573544868623e-39, (32, 3) = -0.6161789643304945e-15, (32, 4) = .0, (32, 5) = -2.272961564215058, (32, 6) = .2}, datatype = float[8], order = C_order); YP := Matrix(32, 6, {(1, 1) = 1.0, (1, 2) = -3.6635195629241393, (1, 3) = 13.421376811728292, (1, 4) = -.20752150850350098, (1, 5) = -0.5702200817365455e-1, (1, 6) = -0.33441406948581164e-4, (2, 1) = .4190953434097267, (2, 2) = -1.5353639315426824, (2, 3) = 5.62483567809648, (2, 4) = -0.8696970293996903e-1, (2, 5) = -0.23805276009511732e-1, (2, 6) = -0.5819729998219887e-5, (3, 1) = .1732188888188128, (3, 2) = -.6345907597520679, (3, 3) = 2.3248355662290145, (3, 4) = -0.3594587012426331e-1, (3, 5) = -0.9823078473142581e-2, (3, 6) = -0.99033781079722e-6, (4, 1) = 0.7055841966143796e-1, (4, 2) = -.25849213901493645, (4, 3) = .9469909655515867, (4, 4) = -0.14642065922226735e-1, (4, 5) = -0.3998584543569432e-2, (4, 6) = -0.1640549659580179e-6, (5, 1) = 0.28304128061312158e-1, (5, 2) = -.10369272213335051, (5, 3) = .3798802987649658, (5, 4) = -0.5873584935447072e-2, (5, 5) = -0.1603562702429767e-2, (5, 6) = -0.2638171316255536e-7, (6, 1) = 0.11172377576572433e-1, (6, 2) = -0.4093022194751972e-1, (6, 3) = .14994866197552117, (6, 4) = -0.2318457134842765e-2, (6, 5) = -0.632896393495785e-3, (6, 6) = -0.410939417418392e-8, (7, 1) = 0.43341769160095515e-2, (7, 2) = -0.158783411959884e-1, (7, 3) = 0.58170610942383204e-1, (7, 4) = -0.8994149456778433e-3, (7, 5) = -0.245512741647959e-3, (7, 6) = -0.6183767474075503e-9, (8, 1) = 0.16343670553362268e-2, (8, 2) = -0.5987535406834639e-2, (8, 3) = 0.2193545209508067e-1, (8, 4) = -0.33915878014610895e-3, (8, 5) = -0.9257831181108378e-4, (8, 6) = -0.8792668070115729e-10, (9, 1) = 0.5944621596263174e-3, (9, 2) = -0.2177823651770427e-2, (9, 3) = 0.7978499188564012e-2, (9, 4) = -0.12336094283919372e-3, (9, 5) = -0.3367292863031933e-4, (9, 6) = -0.1163219861161677e-10, (10, 1) = 0.20765921421315688e-3, (10, 2) = -0.7607635589551353e-3, (10, 3) = 0.2787072053734942e-2, (10, 4) = -0.43092795797985974e-4, (10, 5) = -0.11762693257738654e-4, (10, 6) = -0.14194018114608768e-11, (11, 1) = 0.6930148666691294e-4, (11, 2) = -0.2538873405515502e-3, (11, 3) = 0.9301211964202853e-3, (11, 4) = -0.1438122948094343e-4, (11, 5) = -0.3925524751156479e-5, (11, 6) = -0.158111197895827e-12, (12, 1) = 0.2196474511965646e-4, (12, 2) = -0.8046826976635028e-4, (12, 3) = 0.29479706702331985e-3, (12, 4) = -0.4558055753904399e-5, (12, 5) = -0.12441742279568096e-5, (12, 6) = -0.1589362926141487e-13, (13, 1) = 0.6676964756121347e-5, (13, 2) = -0.24461189888116446e-4, (13, 3) = 0.8961404359576148e-4, (13, 4) = -0.13855830085660227e-5, (13, 5) = -0.378210927593074e-6, (13, 6) = -0.14526894464671326e-14, (14, 1) = 0.19535661469372987e-5, (14, 2) = -0.7156927469988826e-5, (14, 3) = 0.26219542599555274e-4, (14, 4) = -0.4053979851896744e-6, (14, 5) = -0.11065807115009369e-6, (14, 6) = -0.11174533485504098e-15, (15, 1) = 0.5479767419950037e-6, (15, 2) = -0.20075234226639988e-5, (15, 3) = 0.7354600996148526e-5, (15, 4) = -0.1137144332104626e-6, (15, 5) = -0.31039670040614475e-7, (15, 6) = -.0, (16, 1) = 0.14667586063369783e-6, (16, 2) = -0.537349860305963e-6, (16, 3) = 0.1968591635479667e-5, (16, 4) = -0.304377194872888e-7, (16, 5) = -0.8308327702440065e-8, (16, 6) = -0.8595794777543107e-17, (17, 1) = 0.3800160977592546e-7, (17, 2) = -0.13921963448111635e-6, (17, 3) = 0.5100338311760695e-6, (17, 4) = -0.7885976149432237e-8, (17, 5) = -0.2152568060143866e-8, (17, 6) = 0.3438317905933696e-16, (18, 1) = 0.9679561461926475e-8, (18, 2) = -0.3546126115859928e-7, (18, 3) = 0.12991301804768527e-6, (18, 4) = -0.2008672562573159e-8, (18, 5) = -0.5482908363217248e-9, (18, 6) = -0.3438317904608846e-16, (19, 1) = 0.2422302810354404e-8, (19, 2) = -0.887415332982281e-8, (19, 3) = 0.3251063284214716e-7, (19, 4) = -0.502668765575309e-9, (19, 5) = -0.1372090836931743e-9, (19, 6) = 0.17191589521346858e-16, (20, 1) = 0.5953273783129685e-9, (20, 2) = -0.2180993399969996e-8, (20, 3) = 0.7990111619923773e-8, (20, 4) = -0.1235404929511118e-9, (20, 5) = -0.3372175073917995e-10, (20, 6) = -.0, (21, 1) = 0.1449905234394885e-9, (21, 2) = -0.5311755988963094e-9, (21, 3) = 0.1945972104650623e-8, (21, 4) = -0.3008798637050063e-10, (21, 5) = -0.8212565553567704e-11, (21, 6) = 0.25787384281221336e-16, (22, 1) = 0.35141204232587883e-10, (22, 2) = -0.1287404896150451e-9, (22, 3) = 0.4716432733074871e-9, (22, 4) = -0.7292396720459258e-11, (22, 5) = -0.1990620072856783e-11, (22, 6) = -0.8595794760394263e-17, (23, 1) = 0.8475375824080267e-11, (23, 2) = -0.31049713824358454e-10, (23, 3) = 0.11375121626456616e-9, (23, 4) = -0.17587869810663557e-11, (23, 5) = -0.4805349236090068e-12, (23, 6) = -0.4297897380195565e-16, (24, 1) = 0.2035026044727397e-11, (24, 2) = -0.7455373957382428e-11, (24, 3) = 0.27312885648860637e-10, (24, 4) = -0.4223058063671518e-12, (24, 5) = -0.11527367551506473e-12, (24, 6) = -.0, (25, 1) = 0.4878470512049615e-12, (25, 2) = -0.17872647776069955e-11, (25, 3) = 0.65476424299004655e-11, (25, 4) = -0.10124022778070311e-12, (25, 5) = -0.27646144212510994e-13, (25, 6) = -.0, (26, 1) = 0.11680457358602633e-12, (26, 2) = -0.4279624747605665e-12, (26, 3) = 0.15677857117532634e-11, (26, 4) = -0.24242793937901928e-13, (26, 5) = -0.6642889775444323e-14, (26, 6) = -.0, (27, 1) = 0.2792139704425265e-13, (27, 2) = -0.102369938457817e-12, (27, 3) = 0.3749256780921826e-12, (27, 4) = -0.57980686227542876e-14, (27, 5) = -0.11722746662548804e-14, (27, 6) = 0.3438317904156065e-16, (28, 1) = 0.7229355869199076e-14, (28, 2) = -0.26616390820104455e-13, (28, 3) = 0.9732850067357298e-13, (28, 4) = -0.15039585933116824e-14, (28, 5) = -0.3907582220849598e-15, (28, 6) = -.0, (29, 1) = 0.22004123056338692e-14, (29, 2) = -0.8265952539377097e-14, (29, 3) = 0.2999934766469537e-13, (29, 4) = -0.4599587740240465e-15, (29, 5) = -0.1953791110424799e-15, (29, 6) = -0.859579476039015e-17, (30, 1) = 0.7209052523906788e-15, (30, 2) = -0.2945870798181565e-14, (30, 3) = 0.10369578123343452e-13, (30, 4) = -0.15222598804420496e-15, (30, 5) = .0, (30, 6) = -.0, (31, 1) = 0.21108792459646215e-15, (31, 2) = -0.12124057648366197e-14, (31, 3) = 0.38318061401697315e-14, (31, 4) = -0.4534791482086289e-16, (31, 5) = .0, (31, 6) = -.0, (32, 1) = -0.34565573544868623e-39, (32, 2) = -0.6161789643304945e-15, (32, 3) = 0.14005511026010551e-14, (32, 4) = 0.7603642333654124e-40, (32, 5) = .0, (32, 6) = -.0}, datatype = float[8], order = C_order); errproc := proc (x_bvp) local outpoint, X, Y, yout, L, V, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; Digits := 15; outpoint := evalf(x_bvp); X := Vector(32, {(1) = .0, (2) = .23738292772542516, (3) = .4785560381516835, (4) = .7237068936662285, (5) = .9730390563893319, (6) = 1.2267740667509117, (7) = 1.485244856033515, (8) = 1.7514578053505616, (9) = 2.0275186342286915, (10) = 2.314608495795922, (11) = 2.6141654179212277, (12) = 2.9278058961214626, (13) = 3.2528414943537864, (14) = 3.5883120932734123, (15) = 3.935292305144063, (16) = 4.295051734960197, (17) = 4.66370117321776, (18) = 5.036986867849653, (19) = 5.415088268290482, (20) = 5.798104252866241, (21) = 6.18357845672341, (22) = 6.570352338347138, (23) = 6.958439133174796, (24) = 7.347706619144922, (25) = 7.7373742377151125, (26) = 8.12732478470241, (27) = 8.517558877286204, (28) = 8.885300984940212, (29) = 9.205784697647944, (30) = 9.493254557635485, (31) = 9.756201127790266, (32) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(32, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -0.9684278254138667e-13, (1, 4) = 0.24793784560865875e-12, (1, 5) = -0.6074803961513833e-13, (1, 6) = -0.2559292546219694e-15, (2, 1) = 0.16532517766308446e-7, (2, 2) = -0.6056717684239824e-7, (2, 3) = 0.2218890054590015e-6, (2, 4) = -0.34307381915885136e-8, (2, 5) = -0.9392183387136674e-9, (2, 6) = -0.2408512297751391e-12, (3, 1) = 0.56478498238281e-8, (3, 2) = -0.20690990701074774e-7, (3, 3) = 0.758018384288055e-7, (3, 4) = -0.11720072209219468e-8, (3, 5) = -0.3195014467464516e-9, (3, 6) = 0.3656143144594534e-13, (4, 1) = -0.5514557623213443e-11, (4, 2) = 0.20206908133809278e-10, (4, 3) = -0.7402934420152172e-10, (4, 4) = 0.11463005793065814e-11, (4, 5) = 0.4788442881314739e-12, (4, 6) = 0.15156368565892247e-13, (5, 1) = -0.10750717286497465e-8, (5, 2) = 0.393856599359685e-8, (5, 3) = -0.14429012486996655e-7, (5, 4) = 0.22309675540634938e-9, (5, 5) = 0.6089354099132634e-10, (5, 6) = -0.13714292955626477e-15, (6, 1) = -0.6866914044137568e-9, (6, 2) = 0.2515726469981587e-8, (6, 3) = -0.9216412259476526e-8, (6, 4) = 0.1425011669767676e-9, (6, 5) = 0.38877698000868683e-10, (6, 6) = -0.12335124443224783e-14, (7, 1) = -0.23230905524500875e-9, (7, 2) = 0.8510768182345909e-9, (7, 3) = -0.31179361695336254e-8, (7, 4) = 0.48208523985297926e-10, (7, 5) = 0.13144851998407548e-10, (7, 6) = -0.42608996581296306e-15, (8, 1) = -0.33744233921443493e-11, (8, 2) = 0.1237596651318376e-10, (8, 3) = -0.4533943558974563e-10, (8, 4) = 0.7010332403506721e-12, (8, 5) = 0.1863517489136765e-12, (8, 6) = -0.32597874864804974e-15, (9, 1) = 0.6035261538451868e-10, (9, 2) = -0.2210915473113484e-9, (9, 3) = 0.8099732525557996e-9, (9, 4) = -0.12523536363279133e-10, (9, 5) = -0.34244323528565167e-11, (9, 6) = 0.4118892227963015e-16, (10, 1) = 0.52642162004415076e-10, (10, 2) = -0.19284979253083597e-9, (10, 3) = 0.7065089907803169e-9, (10, 4) = -0.109238085521299e-10, (10, 5) = -0.2985816028091057e-11, (10, 6) = 0.7275713364065007e-16, (11, 1) = 0.29102734817932872e-10, (11, 2) = -0.1066007130556671e-9, (11, 3) = 0.39053379416815775e-9, (11, 4) = -0.6038304836406409e-11, (11, 5) = -0.1649927230771947e-11, (11, 6) = 0.5522923898820978e-16, (12, 1) = 0.10938836216895846e-10, (12, 2) = -0.4006148021954623e-10, (12, 3) = 0.14676601478798824e-9, (12, 4) = -0.22692478106265015e-11, (12, 5) = -0.6224970343841889e-12, (12, 6) = 0.19981453259322204e-15, (13, 1) = 0.1577494327091353e-11, (13, 2) = -0.5771435141951299e-11, (13, 3) = 0.2114376611016288e-10, (13, 4) = -0.3269179486933131e-12, (13, 5) = -0.9208225337763152e-13, (13, 6) = 0.1430164415377812e-15, (14, 1) = -0.16572549877025404e-11, (14, 2) = 0.6094888675963528e-11, (14, 3) = -0.2232874254956181e-10, (14, 4) = 0.3452396733161816e-12, (14, 5) = 0.8699402636577551e-13, (14, 6) = -0.9223181910605597e-16, (15, 1) = -0.19922544010413503e-11, (15, 2) = 0.7309010738787319e-11, (15, 3) = -0.2677670258137401e-10, (15, 4) = 0.41401255161124184e-12, (15, 5) = 0.1091726150539443e-12, (15, 6) = .0, (16, 1) = -0.1413231003575007e-11, (16, 2) = 0.5195618033454983e-11, (16, 3) = -0.1903424747293479e-10, (16, 4) = 0.2943012368339272e-12, (16, 5) = 0.7787179461870995e-13, (16, 6) = .0, (17, 1) = -0.8013072141572603e-12, (17, 2) = 0.29490063997697188e-11, (17, 3) = -0.10803742173900677e-10, (17, 4) = 0.16704385302706166e-12, (17, 5) = 0.39982443808968294e-13, (17, 6) = .0, (18, 1) = -0.3902882989883457e-12, (18, 2) = 0.14511241461305278e-11, (18, 3) = -0.5316221477234938e-11, (18, 4) = 0.821975990675695e-13, (18, 5) = 0.20422144231829056e-13, (18, 6) = .0, (19, 1) = -0.17363794645181841e-12, (19, 2) = 0.6429854375582952e-12, (19, 3) = -0.23555896417852147e-11, (19, 4) = 0.3642127274187083e-13, (19, 5) = 0.52017143998469624e-14, (19, 6) = .0, (20, 1) = -0.6718278267234952e-13, (20, 2) = 0.26204028853300927e-12, (20, 3) = -0.9599897034099152e-12, (20, 4) = 0.1484295654133196e-13, (20, 5) = 0.6230621322720747e-15, (20, 6) = .0, (21, 1) = -0.25157775776546026e-13, (21, 2) = 0.9984935160981724e-13, (21, 3) = -0.36580006990891806e-12, (21, 4) = 0.5655783512014042e-14, (21, 5) = -0.4066617257236055e-14, (21, 6) = .0, (22, 1) = -0.35502686011159836e-14, (22, 2) = 0.3602175095655584e-13, (22, 3) = -0.13196643451776997e-12, (22, 4) = 0.20403164532880088e-14, (22, 5) = -0.5396119144289601e-14, (22, 6) = .0, (23, 1) = 0.10284508286104878e-14, (23, 2) = 0.12411539569819745e-13, (23, 3) = -0.4546999720190479e-13, (23, 4) = 0.7029285327698647e-15, (23, 5) = -0.7423652305785155e-15, (23, 6) = .0, (24, 1) = 0.173773594942215e-14, (24, 2) = 0.4112916487599153e-14, (24, 3) = -0.1506788151037804e-13, (24, 4) = 0.2328524844886688e-15, (24, 5) = -0.1856238287719891e-14, (24, 6) = .0, (25, 1) = 0.4344027029528252e-14, (25, 2) = 0.13196997514001117e-14, (25, 3) = -0.48349641384560675e-14, (25, 4) = 0.7462623553487176e-16, (25, 5) = -0.22193824282029186e-14, (25, 6) = .0, (26, 1) = 0.4460989674965387e-14, (26, 2) = 0.41194936326503473e-15, (26, 3) = -0.15095495409304056e-14, (26, 4) = 0.2320252873697474e-16, (26, 5) = -0.32766498475707286e-14, (26, 6) = .0, (27, 1) = 0.3696416138591636e-14, (27, 2) = 0.12549891970606628e-15, (27, 3) = -0.4603820220215734e-15, (27, 4) = 0.6975707272173805e-17, (27, 5) = -0.7039297413666171e-14, (27, 6) = .0, (28, 1) = 0.32766498475707286e-14, (28, 2) = 0.3929748094167081e-16, (28, 3) = -0.14497552584139333e-15, (28, 4) = 0.20985078767629603e-17, (28, 5) = -0.2715448065496867e-14, (28, 6) = .0, (29, 1) = 0.4191157171111337e-14, (29, 2) = 0.13487084044367167e-16, (29, 3) = -0.50969983278108777e-16, (29, 4) = 0.6505062556230812e-18, (29, 5) = -0.2715448065496867e-14, (29, 6) = .0, (30, 1) = 0.2715448065496867e-14, (30, 2) = 0.47867321313024425e-17, (30, 3) = -0.19848217818157185e-16, (30, 4) = 0.18189739941528604e-18, (30, 5) = -0.2715448065496867e-14, (30, 6) = .0, (31, 1) = 0.2715448065496867e-14, (31, 2) = 0.14776211487867332e-17, (31, 3) = -0.8731601790873086e-17, (31, 4) = 0.3127759816314512e-19, (31, 5) = -0.2715448065496867e-14, (31, 6) = .0, (32, 1) = 0.2715448065496867e-14, (32, 2) = 0.3600580577590624e-39, (32, 3) = -0.46433170515282995e-17, (32, 4) = .0, (32, 5) = -0.2715448065496867e-14, (32, 6) = .0}, datatype = float[8], order = C_order); if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [6, 32, [f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(6, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(6, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(32, 6, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)]'[i] = yout[i], i = 1 .. 6)] end proc; if not type(outpoint, 'numeric') then if outpoint = "start" or outpoint = "left" then return X[1] elif outpoint = "method" then return "bvp" elif outpoint = "right" then return X[32] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.218890054590015e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [6, 32, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[32] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[32] end if; if Digits <= trunc(evalhf(Digits)) and (_EnvInFsolve <> true or _EnvDSNumericSaveDigits <= trunc(evalhf(Digits))) then V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = .0, (1, 2) = .0, (2, 1) = .0, (2, 2) = .0, (3, 1) = .0, (3, 2) = .0, (4, 1) = .0, (4, 2) = .0, (5, 1) = .0, (5, 2) = .0, (6, 1) = .0, (6, 2) = .0, (7, 1) = .0, (7, 2) = .0}, datatype = float[8], order = C_order); yout := Vector(6, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, var(yout), var(L), var(V))) else if _EnvInFsolve = true then Digits := _EnvDSNumericSaveDigits end if; V := array( 1 .. 6, [( 1 ) = (7), ( 2 ) = (0), ( 3 ) = (false), ( 4 ) = (false), ( 5 ) = (false), ( 6 ) = (false)  ] ); L := Matrix(7, 2, {(1, 1) = 0., (1, 2) = 0., (2, 1) = 0., (2, 2) = 0., (3, 1) = 0., (3, 2) = 0., (4, 1) = 0., (4, 2) = 0., (5, 1) = 0., (5, 2) = 0., (6, 1) = 0., (6, 2) = 0., (7, 1) = 0., (7, 2) = 0.}, order = C_order); yout := Vector(6, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0., (6) = 0.}); `dsolve/numeric/hermite`(32, 6, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 6)] end proc, (2) = Array(1..7, {(1) = 18446744074221990414, (2) = 18446744074221990590, (3) = 18446744074221990766, (4) = 18446744074221990942, (5) = 18446744074221991118, (6) = 18446744074221991294, (7) = 18446744074221991470}), (3) = [eta, f(eta), diff(f(eta), eta), diff(diff(f(eta), eta), eta), F(eta), G(eta), H(eta)], (4) = 0}); solnproc := data[1]; if not type(outpoint, 'numeric') then if outpoint = "solnprocedure" then return eval(solnproc) elif member(outpoint, ["start", "left", "right", "errorproc", "rawdata", "order", "error"]) then return solnproc(eta) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(eta) else `H(eta)` := pointto(data[2][7]); return ('`H(eta)`')(eta) end if end if; try res := solnproc(outpoint); res[7] catch: error  end try end proc], [eta, f(eta)], 0 .. 10)

(7)

``

(8)

print([(Y || (1 .. 3))(0)]);

[HFloat(0.0662575289978352), HFloat(0.06239249313847126), HFloat(0.05664455547330386)]

(9)

print([(YP || (1 .. 3))(0)]);

[HFloat(-2.308757932969589), HFloat(-2.2878028202715557), HFloat(-2.2574484928181637)]

(10)

print([(YR || (1 .. 3))(0)]);

[HFloat(0.20000866382583435), HFloat(0.20000675928400788), HFloat(0.2000045400222304)]

(11)

odeplots([Y || (1 .. 1)], 0 .. 10, labels = [eta, F(eta)]):

``


Download hydro92.mw

i am trying to solve 6 ODE with boundary condition


restart

with*plots

with*plots

(1)

Eq1 := (1-theta(eta)/theta[r])*(diff(f(eta), eta, eta, eta))+(diff(f(eta), eta, eta))*(diff(theta(eta), eta))/theta[r]+(1-theta(eta)/theta[r])^2*(f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta)))) = 0

(1-theta(eta)/theta[r])*(diff(diff(diff(f(eta), eta), eta), eta))+(diff(diff(f(eta), eta), eta))*(diff(theta(eta), eta))/theta[r]+(1-theta(eta)/theta[r])^2*(f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta)))) = 0

(2)

Eq2 := G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0

G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0

(3)

Eq3 := G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0

G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0

(4)

Eq4 := G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0

G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0

(5)

Eq5 := (1+s*theta(eta))*(diff(theta(eta), eta, eta))+(diff(theta(eta), eta))^2*s+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta))+(2/3)*B*H(eta)*(theta[p](eta)-theta(eta)) = 0

(1+s*theta(eta))*(diff(diff(theta(eta), eta), eta))+(diff(theta(eta), eta))^2*s+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta))+(2/3)*B*H(eta)*(theta[p](eta)-theta(eta)) = 0

(6)

Eq6 := 2*F(eta)*theta[p](eta)+G(eta)*(diff(theta[p](eta), eta))+L0*B*(theta[p](eta)-theta(eta)) = 0

2*F(eta)*theta[p](eta)+G(eta)*(diff(theta[p](eta), eta))+L0*B*(theta[p](eta)-theta(eta)) = 0

(7)

bcs1 := f(0) = 0, (D(f))(0) = 1, (D(f))(10) = 0;

f(0) = 0, (D(f))(0) = 1, (D(f))(10) = 0

(8)

fixedparameter := [M = .5, B = .5, theta[r] = -10, L0 = 1, s = .1, Pr = 1];

[M = .5, B = .5, theta[r] = -10, L0 = 1, s = .1, Pr = 1]

(9)

Eq7 := eval(Eq1, fixedparameter);

(1+(1/10)*theta(eta))*(diff(diff(diff(f(eta), eta), eta), eta))-(1/10)*(diff(diff(f(eta), eta), eta))*(diff(theta(eta), eta))+(1+(1/10)*theta(eta))^2*(f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-.5*(diff(f(eta), eta))+.5*H(eta)*(F(eta)-(diff(f(eta), eta)))) = 0

(10)

Eq8 := eval(Eq2, fixedparameter);

G(eta)*(diff(F(eta), eta))+F(eta)^2+.5*F(eta)-.5*(diff(f(eta), eta)) = 0

(11)

Eq9 := eval(Eq3, fixedparameter);

G(eta)*(diff(G(eta), eta))+.5*f(eta)+.5*G(eta) = 0

(12)

Eq10 := eval(Eq5, fixedparameter);

(1+.1*theta(eta))*(diff(diff(theta(eta), eta), eta))+.1*(diff(theta(eta), eta))^2+f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta)+.3333333333*H(eta)*(theta[p](eta)-theta(eta)) = 0

(13)

Eq11 := eval(Eq6, fixedparameter);

2*F(eta)*theta[p](eta)+G(eta)*(diff(theta[p](eta), eta))+.5*theta[p](eta)-.5*theta(eta) = 0

(14)

bcs2 := F(10) = 0;

F(10) = 0

(15)

bcs3 := G(10) = -f(10);

G(10) = -f(10)

(16)

bcs4 := H(10) = n;

H(10) = n

(17)

bcs5 := theta(10) = 0;

theta(10) = 0

(18)

bcs6 := theta[p](10) = 0;

theta[p](10) = 0

(19)

L := [.2];

[.2]

(20)

for k to 1 do R := dsolve(eval({Eq10, Eq11, Eq4, Eq7, Eq8, Eq9, bcs1, bcs2, bcs3, bcs4, bcs5, bcs6}, n = L[k]), [f(eta), F(eta), G(eta), H(eta), theta(eta), theta[p](eta)], numeric, output = listprocedure); Y || k := rhs(R[5]); YP || k := rhs(R[6]); YJ || k := rhs(R[7]); YS || k := rhs(R[2]) end do

``


Download hydro.mw

restart

with*plots

with*plots

(1)

Eq1 := (1-theta(eta)/theta[r])*(diff(f(eta), eta, eta, eta))+(diff(f(eta), eta, eta))*(diff(theta(eta), eta))/theta[r]+(1-theta(eta)/theta[r])^2*(f(eta)*(diff(f(eta), eta, eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta)))) = 0

(1-theta(eta)/theta[r])*(diff(diff(diff(f(eta), eta), eta), eta))+(diff(diff(f(eta), eta), eta))*(diff(theta(eta), eta))/theta[r]+(1-theta(eta)/theta[r])^2*(f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-M*(diff(f(eta), eta))+B*H(eta)*(F(eta)-(diff(f(eta), eta)))) = 0

(2)

Eq2 := G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0

G(eta)*(diff(F(eta), eta))+F(eta)^2+B*(F(eta)-(diff(f(eta), eta))) = 0

(3)

Eq3 := G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0

G(eta)*(diff(G(eta), eta))+B*(f(eta)+G(eta)) = 0

(4)

Eq4 := G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0

G(eta)*(diff(H(eta), eta))+H(eta)*(diff(G(eta), eta))+F(eta)*H(eta) = 0

(5)

Eq5 := (1+s*theta(eta))*(diff(theta(eta), eta, eta))+(diff(theta(eta), eta))^2*s+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta))+(2/3)*B*H(eta)*(theta[p](eta)-theta(eta)) = 0

(1+s*theta(eta))*(diff(diff(theta(eta), eta), eta))+(diff(theta(eta), eta))^2*s+Pr*(f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta))+(2/3)*B*H(eta)*(theta[p](eta)-theta(eta)) = 0

(6)

Eq6 := 2*F(eta)*theta[p](eta)+G(eta)*(diff(theta[p](eta), eta))+L0*B*(theta[p](eta)-theta(eta)) = 0

2*F(eta)*theta[p](eta)+G(eta)*(diff(theta[p](eta), eta))+L0*B*(theta[p](eta)-theta(eta)) = 0

(7)

bcs1 := f(0) = 0, (D(f))(0) = 1, (D(f))(10) = 0;

f(0) = 0, (D(f))(0) = 1, (D(f))(10) = 0

(8)

fixedparameter := [M = .5, B = .5, theta[r] = -10, L0 = 1, s = .1, Pr = 1];

[M = .5, B = .5, theta[r] = -10, L0 = 1, s = .1, Pr = 1]

(9)

Eq7 := eval(Eq1, fixedparameter);

(1+(1/10)*theta(eta))*(diff(diff(diff(f(eta), eta), eta), eta))-(1/10)*(diff(diff(f(eta), eta), eta))*(diff(theta(eta), eta))+(1+(1/10)*theta(eta))^2*(f(eta)*(diff(diff(f(eta), eta), eta))-(diff(f(eta), eta))^2-.5*(diff(f(eta), eta))+.5*H(eta)*(F(eta)-(diff(f(eta), eta)))) = 0

(10)

Eq8 := eval(Eq2, fixedparameter);

G(eta)*(diff(F(eta), eta))+F(eta)^2+.5*F(eta)-.5*(diff(f(eta), eta)) = 0

(11)

Eq9 := eval(Eq3, fixedparameter);

G(eta)*(diff(G(eta), eta))+.5*f(eta)+.5*G(eta) = 0

(12)

Eq10 := eval(Eq5, fixedparameter);

(1+.1*theta(eta))*(diff(diff(theta(eta), eta), eta))+.1*(diff(theta(eta), eta))^2+f(eta)*(diff(theta(eta), eta))-(diff(f(eta), eta))*theta(eta)+.3333333333*H(eta)*(theta[p](eta)-theta(eta)) = 0

(13)

Eq11 := eval(Eq6, fixedparameter);

2*F(eta)*theta[p](eta)+G(eta)*(diff(theta[p](eta), eta))+.5*theta[p](eta)-.5*theta(eta) = 0

(14)

bcs2 := F(10) = 0;

F(10) = 0

(15)

bcs3 := G(10) = -f(10);

G(10) = -f(10)

(16)

bcs4 := H(10) = n;

H(10) = n

(17)

bcs5 := theta(10) = 0;

theta(10) = 0

(18)

bcs6 := theta[p](10) = 0;

theta[p](10) = 0

(19)

L := [.2];

[.2]

(20)

for k to 1 do R := dsolve(eval({Eq10, Eq11, Eq4, Eq7, Eq8, Eq9, bcs1, bcs2, bcs3, bcs4, bcs5, bcs6}, n = L[k]), [f(eta), F(eta), G(eta), H(eta), theta(eta), theta[p](eta)], numeric, output = listprocedure); Y || k := rhs(R[5]); YP || k := rhs(R[6]); YJ || k := rhs(R[7]); YS || k := rhs(R[2]) end do

``


then i get this error

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

i dont know where i need to change after view it one by one..

Download hydro.mw

I am having trouble printing out a limit cylce on maple 16.  I have the attached file and if anybody could look at it and perhaps help me out it would be greatly appreciated.  The first limit cycle is supposed to look somewhat like the second one.  I'v tried many different things but nothing seems to be working.  an explenation would also be nice too.  if the file does not open correctly also let me know. thank you very much.  

 Math_4710_Hilbert_16.mw

Hi all

I dont know why some Z1 appears on the screen and the code does not converge.
please help me
thanks alooooot


restart;
n:=3;
nn:=3;
m:=1;
BB:=1;
BINF:=5:
pr:=7;
digits:=10;
>
eq1:=diff(f(tau),tau$3)+((3/5)*f(tau)*diff(f(tau),tau$2))-(1/5)*(diff(f(tau),tau$1))^2+((2/5)*tau*diff(h(tau),tau$1))-((2/5)*h(tau))-BB*diff(f(tau),tau$1)=0;
eq11:=(1/pr)*diff(h(tau),tau$3)+(3/5)*f(tau)*diff(h(tau),tau$2)=0;

h(tau):=sum(p^i*h[i](tau),i=0..nn);
f(tau):=sum(p^i*f[i](tau),i=0..n);

 

H1:= p*(diff(f(tau),tau$3)+((3/5)*f(tau)*diff(f(tau),tau$2))-(1/5)*(diff(f(tau),tau$1))^2+((2/5)*tau*diff(h(tau),tau$1))-((2/5)*h(tau))-BB*diff(f(tau),tau$1))+(1-p)*(diff(f(tau),tau$3)):
H11:= p*((1/pr)*diff(h(tau),tau$3)+(3/5)*f(tau)*diff(h(tau),tau$2))+(1-p)*(diff(h(tau),tau$3)):
>
eq2:=simplify(H1):
eq22:=simplify(H11):
eq3:=collect(expand(eq2),p):
eq33:=collect(expand(eq22),p):
eq4:=
convert(series(collect(expand(eq2), p), p, n+1), 'polynom');
eq44:=
convert(series(collect(expand(eq22), p), p, n+1), 'polynom');
for i to n do
s[i] := coeff(eq4, p^i) ;
print (i);
end do:
for i to nn do
ss[i] := coeff(eq44, p^i) ;
print (i);
end do:
s[0]:=diff(f[0](tau), tau$3);
ss[0]:=diff(h[0](tau), tau$3);
ics[0]:=f[0](0)=0, D(f[0])(0)=0, D(f[0])(BINF)=0;
icss[0]:=h[0](BINF)=0, D(h[0])(0)=1, D(h[0])(BINF)=0;

dsolve({s[0], ics[0]});
f[0](tau):= rhs(%);
#dsolve({ss[0], icss[0]});
h[0](tau):= -exp(-tau); #;rhs(%);

>
>
for i to n do
f[ii-1](tau):=convert(series(f[ii-1](tau), tau, nn+1), 'polynom');
h[ii-1](tau):=convert(series(h[ii-1](tau), tau, nn+1), 'polynom');
s[i]:=simplify((s[i]));
ics[i]:=f[i](0)=0, D(f[i])(0)=0, D(f[i])(BINF)=0;
dsolve({s[i], ics[i]});
f[i](tau):=rhs(%);
ss[i]:=(ss[i]);
icss[i]:=h[i](BINF)=0, D(h[i])(0)=0, D(h[i])(BINF)=0;
dsolve({ss[i], icss[i]});
h[i](tau):=rhs(%);

end do;

f(tau):=sum((f[j])(tau),j=0..n);
with(numapprox):

 

plot(diff(f(tau),tau),tau=0..5,color=blue,style=point,symbol=circle,symbolsize=7,labels=["tau","velocity"]);
plot(pade(diff(f(tau),tau), tau, [7, 7]),tau=0..5,color=blue,style=point,symbol=circle,symbolsize=7,labels=["tau","velocity"]);

 

 

I'm trying to plot the direction field of the second order differential equation x''=x'-cos(x) using dfieldplot: 

> with(DEtools); with(plots);
> f1 := (x, y) options operator, arrow; diff(x(t), t)-cos(x(t)) end proc;
/ d \
(x, y) -> |--- x(t)| - cos(x(t))
\ dt /
> dfieldplot([diff(x(t), t) = y(t), diff(y(t), t) = f1(x(t), y(t))], [x(t), y(t)], t = -2 .. 2, x = -2 .. 2, y = -2 .. 2);
Error, (in DEtools/dfieldplot) cannot produce plot, non-autonomous DE(s) require initial conditions.
>

The error I'm getting says I need initial conditions, but I wasn't provided with any. Is there another way to plot this? Sorry if this is dumb question, but I've only ever plotted first order equations.

restart:

ODE:=diff((-diff(u(y),y))^n,y)=A;

bcs:=D(u)(0)=0,u(h)=0;

dsolve({ODE,bcs});

             u(y) = 0

 

Hello everyone, 

I have a problem solving with ODE's system solving. I have 2 equation and 4 initial  conditions. When i calculate like that,u can look this file.  beamsolvingfortim.mw. It is working it is giving me T1 and T2 equations depends on time. 

 

 In 2. system which i have a problem i want to calculate this equations depends on x(displacement). I have again 2 equation and 4 boundry conditions. it is solving the ODE'S system without boundry conditions. (It is giving with C1 C2 C3 and I)Problem is when i want to find its values with boundry conditions it is not giving a result. Is there a problem with complex number(I) or boundry conditions are not enough?   

 

> evalf(dsolve({sys}));

{X1s(x) = -3.060206320 + _C1 exp(-0.3487988669 x)

+ _C2 exp(0.3487988669 x) + _C3 exp(-0.3563227426 I x), X2s(x) =

-0.6321326989 _C1 exp(-0.3487988669 x)

+ 0.6321326989 _C2 exp(0.3487988669 x)

- 0.6053448484 I _C3 exp(-0.3563227426 I x)}

When i write like that, nothing is happening. I also upload the files. If u can help , i would be really appreciate. 

eq2 := dsolve({A, B, bc}, [X1s(x), X2s(x)])

beamsolving(thick.mw

 

 

Dear all;

Please I need your help to find the error in my code.

I want to solve an ode, with condition on step size.

ode := diff(y(x), x) = 2*x+y(x);
f:=(x,y)->2*x-y;

analyticsol := rhs(dsolve({ode, y(0) = 1}));
RKadaptivestepsize := proc (f, a, b, epsilon, N)
local x, y, n, h,k,z,R,p;
p:=2;
h := evalf(b-a)/N; ## we begin with this setpsize
x[0] := a; y[0] := 1; ## Initialisation
for n from 0 to N-1 do  ##loop
x[n+1] := a+(n+1)*h;  ## noeuds
k[1] := f(x[n], y[n]);
k[2] := f(x[n]+h, y[n]+h*k[1]);
k[3] := f(x[n]+h/2, y[n]+h/4*(k[1]+k[2]));
z[n+1] := z[n]+(h/2)*(k[1]+k[2]);## 2-stage runge Kutta.
y[n+1] := y[n]+(h/6)*(k[1]+k[2]+4*k[3]);
R:=abs(y[n+1]-z[n+1]); ## local erreur
hstar:=sqrt(epsilon/R)
if R=<=epsilon    then
   x[n] := x[n+1]+h;
   y[n]:=y[n+1];
   n:=n+1;

else

h:=hstar;
end if
 end do;
[seq([x[n], y[n]], n = 0 .. N)];
[seq([x[n], z[n]], n = 0 .. N)];
end proc:

epsilon:=1e-8;
RKadaptivestepsize((x,y)->2*x-y,0,1, epsilon,20)

Hi.

Please, I need a code in maple for adaptative setp size control for runge Kutta.

Thank you.

Dear all,

Thank you for your Help.

h: stepsize;

x in [0,x0];

I give all the step of my code, but I think there is a mistake. I wait for your Help.

I would like to compute the error between  Method Huen with step size h and step size 2h using the definition of epsilon given below:

 ## The error written epsilon(x0,h)= sqrt(1/(N+1) * sum_i=0^N  (y_i^{2h}-y_(2i)^h)^2 ), where y_i^(2h) is the approximation of y(i*2*h).

 ## We want : loglog epsilon versus h.

  epsilon:=(x0,h)->sqrt( 1/(N+1)*add( (Heun1(f,x0,i)-Heun2(f,x0,i))^2,i=0..N ) );

  f:=(x,y)=1/(1+cos(y)); 

  ode:=diff(y(x),x)=f(x,y);

ic:=y(0)=1;  h:=x0/(2*N);

## Method Heun with step size 2h

> Heun1 := proc (f, x0,)

local x, y, i, h, k;

y := Array(0 .. N);

x := Array(0 .. N);

h := evalf((1/2)*x0/N);

x[0] := 0;

y[0] := 1;

for i from 0 to N do

x[i+1] := (2*i+2)*h;

k[1] := f(x[i], y[i]);

k[2] := f(x[i]+h, y[i]+h*k[1]);

y[i+1] := y[i]+h*((1/2)*k[1]+(1/2)*k[2]);

end do;

[seq([x[i], y[i]], i = 0 .. N)];

end proc;

### Now Heun with step size h  ( the same h)

> Heun2 := proc (f, x0,)

local x, y, i, h, k;

y := Array(0 .. N);

x := Array(0 .. N);

h := evalf((1/2)*x0/N);

x[0] := 0;

y[0] := 1;

for i from 0 to N do

x[i+1] := (i+1)*h;

k[1] := f(x[i], y[i]);

k[2] := f(x[i]+h, y[i]+h*k[1]);

y[i+1] := y[i]+h*((1/2)*k[1]+(1/2)*k[2]);

end do;

[seq([x[2*i], y[2*i]], i = 0 .. N)];

end proc;

 

 

Thanks you for your help.


                                

                        

 

Dear collegues

I wrote the following code

 


restart:
Digits := 15;
a[k]:=0;
b[k]:=7.47;
a[mu]:=39.11;
b[mu]:=533.9;
mu[bf]:=9.93/10000;
k[bf]:=0.597;
ro[p]:=3880 ;
ro[bf]:= 998.2;
c[p]:= 773;
c[bf]:= 4182;
#mu[bf]:=1;
Gr[phi]:=0; Gr[T]:=0;
#dp:=0.1;
Ree:=1;
Pr:=1;
Nbt:=cc*NBTT+(1-cc^2)*6;

#######################
slip:=0.1;         ####
NBTT:=2;           ####
lambda:=0.1;       ####
phi_avg:=0.02;    ####
#######################


eq1:=diff( (1+a[mu]*phi(eta)+b[mu]*phi(eta)^2)*diff(u(eta),eta),eta)+dp/mu[bf]+Gr[T]*T(eta)-Gr[phi]*phi(eta);
eq2:=diff((1+a[k]*phi(eta)+b[k]*phi(eta)^2)*diff(T(eta),eta),eta)+lambda*T(eta)/k[bf];
eq3:=diff(phi(eta),eta)+1/Nbt*diff(T(eta),eta);
Q:=proc(pp2,fi0) local res,F0,F1,F2,a,INT0,INT10;
global Q1,Q2;
print(pp2,fi0);
if not type([pp2,fi0],list(numeric)) then return 'procname(_passed)' end if:
res := dsolve({subs(dp=pp2,eq1)=0,eq2=0,eq3=0,u(0)=slip*D(u)(0),u(1)=-slip*D(u)(1),D(T)(0)=0,D(T)(1)=1,phi(0)=fi0}, numeric,output=listprocedure,continuation=cc);
F0,F1,F2:=op(subs(res,[u(eta),phi(eta),T(eta)])):
INT0:=evalf(Int(F0(eta),eta=0..1));
INT10:=evalf(Int(F0(eta)*F1(eta),eta=0..1));
a[1]:=evalf(Int(F0(eta),eta=0..1))-Ree*Pr;;
a[2]:=INT10/INT0-phi_avg;
Q1(_passed):=a[1];
Q2(_passed):=a[2];
if type(procname,indexed) then a[op(procname)] else a[1],a[2] end if
end proc;
Q1:=proc(pp2,fi0) Q[1](_passed) end proc;
Q2:=proc(pp2,fi0) Q[2](_passed) end proc;
Optimization:-LSSolve([Q1,Q2],initialpoint=[0.3,0.0007]);




se:=%[2];
res2 := dsolve({subs(dp=se[1],eq1)=0,eq2=0,eq3=0,u(0)=slip*D(u)(0),u(1)=-slip*D(u)(1),D(T)(0)=0,D(T)(1)=1,phi(0)=se[2]}, numeric,output=listprocedure,continuation=cc);
G0,G1,G2:=op(subs(res2,[u(eta),phi(eta),T(eta)])):
TTb:=evalf(Int(G0(eta)*G2(eta)*(G1(eta)*ro[p]*c[p]+(1-G1(eta))*ro[bf]*c[bf] ),eta=0..1))/evalf(Int(G0(eta)*(G1(eta)*ro[p]*c[p]+(1-G1(eta))*ro[bf]*c[bf] ),eta=0..1));
with(plots):
odeplot(res2,[[eta,phi(eta)/phi_avg]],0..1);
odeplot(res2,[[eta,T(eta)/TTb]],0..1);
odeplot(res2,[[eta,u(eta)/(Ree*Pr)]],0..1);

res2(1);
Nuu:=(1/TTb);
1/((1+a[k]*G1(1)+b[k]*G1(1)^2)/(1+a[k]*phi_avg+b[k]*phi_avg^2));
(1/TTb)*(((1+a[k]*G1(1)+b[k]*G1(1)^2)/(1+a[k]*phi_avg+b[k]*phi_avg^2)));
>

I want to run the code for the value of NBTT in the range of 0.2 to 10. this code gave the results in the range of 4-10 easily. So, I used the continuation which improve the range of the results between 2-10. However, I coudnt gave the results when 0.2<NBTT<2. Would you please help me in this situation.

Also, It is to be said that the values of phi should be positive. in some ranges, I can see that phi(1) is negative. Can I place a condition in which the values phi restricted to be positive.

Thanks for your attentions in advance

Amir

Dear all;

Than you for help.

how  many steps are required to achieve a error of 1.e-3 in the numerical value of y(1).

Here The 3 -step procedure  Range Kutta Method.

## Exact  solution  

### We will modifty N ( number of steps to get error =10^(-3). )

 

## Procedure Range Kutta

> RK3 := proc (f, a, b, y0, N)

local x, y, n, h, k, vectRK3;

y := Array(0 .. N);

x := Array(0 .. N);

h := evalf(b-a)/N;

x[0] := a; y[0] := 1;

for n from 0 to N-1 do

x[n+1] := a+(n+1)*h;

k[1] := f(x[n], y[n]);

k[2] := f(x[n]+(1/2)*h, y[n]+(1/2)*h*k[1]);

k[3] := f(x[n]+h, y[n]+h*(-k[1]+2*k[2]));

y[n+1] := y[n]+(1/6)*h*(k[1]+4*k[2]+k[3])

end do;

[seq([x[n], y[n]], n = 0 .. N)]; y[1];

end proc;

## Now  we compute the error between y(1) and exact  solution for different value of  N

### I have a problem in this part


 errorRk3 := array(1 .. 29);
 for N from  2 to 30 do

errorrRk3[N] := abs(eval(rhs(res), x = 1)-RK3((x,y)->-y,0,1,N));

if errorrRk3[N] =10^{-3} end ;
end  do ;

 

 

restart:

Eq1:=diff(f(x),x)=1;

f:=1:

plot(1,x=0..10);

cs:=(f)(0)=0;

p:=dsolve({Eq1,cs},numeric);

odeplot(p, [x,diff(f(x),x)], 0..10);

why I cannot get a plot diff(f(x),x) like this?

 

whats going on here?

 

 

 

Dear all;

Please Have some one an idea to transform or convert 2nd order ODE to system of First ODE ( of course using maple).

Thanks

 

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