Items tagged with bvp


 

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refresh

(1)

G := 6.6743*10^(-8); 1; c := 2.99792458*10^10; 1; pi := 3.143; 1; rho := 5.3808*10^14

0.6674300000e-7

 

0.2997924580e11

 

3.143

 

0.5380800000e15

(2)

diff(P(r), r) = -G*(rho*c^2+P(r))*((4*pi*r^3*(1/3))*rho+4*Pi*r^3*P(r)/c^2)/(c^2*(r^2-2*G*r*(4*pi*r^3*(1/3))*rho/c^2)), diff(v(r), r) = 1.485232054*10^(-28)*((4*pi*r^3*(1/3))*rho+4.450600224*10^(-21)*Pi*r^3*P(r))/(r^2-1.485232054*10^(-28)*r*(4*pi*r^3*(1/3))*rho)

diff(P(r), r) = -0.7426160269e-28*(0.4836021866e36+P(r))*(0.2254913920e16*r^3+0.4450600224e-20*Pi*r^3*P(r))/(r^2-0.3349070432e-12*r^4), diff(v(r), r) = 0.1485232054e-27*(0.2254913920e16*r^3+0.4450600224e-20*Pi*r^3*P(r))/(r^2-0.3349070432e-12*r^4)

(3)

condition; -1; P(0) = 0, v(1014030) = -.4283

P(0) = 0, v(1014030) = -.4283

(4)

``


 

Download maple_soft.mw

I found the solution of P(r) at P(0)=0, but could obtain the result of v(r) at v(1014030)=-0.4283, v(r) may have a graph such that i can goes from -0.4283 to 0.

G := 6.6743*10^(-8);

a := 1.9501*10^24;

b := .3306;

c := 2.99792458*10^10;

d := 2.035;

pi := 3.143;

eps := 3.8220*10^35;

g(r) = 1-s(r)/0.06123;

j(r) = e^(-(1/2)*w(r))*(1-2*G*v(r)/(r*c^2))^.5

sys := diff(v(r), r) = 4*pi*r^2*eps/c^2, ics=v(0)=0

diff(u(r), r) = -G*(eps+u(r))*(v(r)+4*Pi*r^3*u(r)/c^2)/(c^2*(r^2-2*G*r*v(r)/c^2)),u(0)=1.3668*10^34

diff(w(r), r) = 1.485232054*10^(-28)*(v(r)+4.450600224*10^(-21)*pi*r^3*u(r))/(r^2-2*G*r*v(r)/c^2), conditions: w(0)=0,iterate it to find w(688240)=-2.05684, it solve must satistfy the both conditions.

diff(r^4*j(r)*(diff(g(r), r)), r)+4*r^3*g(r)*(diff(j(r), r)) = 0, conditions dg(r)/dr =0  at r=0, g(688240) =0.87214

diff(J(r), r) = (8*pi*(1/3))*(eps/c^2+u(r)/c^2)*(g(r)*j(r).(r^4))/(1-2*G*v(r)/(r*c^2)) condition J(0)=0.

Dear sir in this problem should accept five boundaryconditions but it is not working for five boundary conditions and showing the following error please can you tell why it is like this ??

Error, (in dsolve/numeric/bvp/convertsys) too many boundary conditions: expected 4, got 5
Error, (in plots:-display) expecting plot structures but received: [fplt[1], fplt[2], fplt[3], fplt[4], fplt[5], fplt[6], fplt[7]]
Error, (in plots:-display) expecting plot structures but received: [tplt[1], tplt[2], tplt[3], tplt[4], tplt[5], tplt[6], tplt[7]]
 

and for the progam please check the following link

stretching_cylinder_new1.mw

Please anyone, I have been battling with this problem for a while yet the error message keeps coming. Would be happy if responded to.

Thanks 
 

NULL

restart

Digits := 10

with(ODETools)

with(student)

with(plots)

inf := 4.2

NULL

equ1 := diff(f[0](eta), `$`(eta, 3))+theta[0](eta) = 0

equ2 := diff(theta[0](eta), `$`(eta, 2))+3*f[0](eta)*(diff(theta[0](eta), eta)) = 0

Bcs1 := f[0](0) = 0, (D(f[0]))(0) = 0, theta[0](0) = 1, theta[0](inf) = 0, (D(D(f[0])))(inf) = 0

S1 := dsolve({Bcs1, equ1, equ2}, {f[0](eta), theta[0](eta)}, type = numeric)

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) 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(21, {(1) = .0, (2) = .19993050946471785, (3) = .40078377746315347, (4) = .6025727748609847, (5) = .805792602032412, (6) = 1.010942304650061, (7) = 1.2180763336987108, (8) = 1.4270038908463605, (9) = 1.6375902221831404, (10) = 1.8498543724186098, (11) = 2.0633079120179274, (12) = 2.277741391439103, (13) = 2.4931129139047408, (14) = 2.7089887386097495, (15) = 2.9252757828996607, (16) = 3.1419082091550377, (17) = 3.3586565343807853, (18) = 3.5755020065597023, (19) = 3.7897835066856795, (20) = 3.99778821105096, (21) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(21, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .8245101724754578, (1, 4) = 1.0, (1, 5) = -.7109880345825436, (2, 1) = 0.15194130384185354e-1, (2, 2) = .14580548143397778, (2, 3) = .6387850483082825, (2, 4) = .857963238913636, (2, 5) = -.7087869877011237, (3, 1) = 0.5625387147295941e-1, (3, 2) = .2577556073775664, (3, 3) = .4806893773780191, (3, 4) = .7167515674300292, (3, 5) = -.6944757971749999, (4, 1) = .11711872046127954, (4, 2) = .34110224456170846, (4, 3) = .3499979513587831, (4, 4) = .5797495081496531, (4, 5) = -.6595302165926753, (5, 1) = .19289982468547776, (5, 2) = .4011617938545637, (5, 3) = .24543411078038904, (5, 4) = .4513251759894287, (5, 5) = -.6004288125540566, (6, 1) = .2797565188640971, (6, 2) = .4428520778243424, (6, 3) = .16494373679100188, (6, 4) = .3361497197458259, (6, 5) = -.5193790217421129, (7, 1) = .37456519619918616, (7, 2) = .4705413231882741, (7, 3) = .10579089990103963, (7, 4) = .23830615973840436, (7, 5) = -.4239568572171149, (8, 1) = .4748530263492926, (8, 2) = .48804935564305746, (8, 3) = 0.6453023961994517e-1, (8, 4) = .16012402142182885, (8, 5) = -.3249339143694787, (9, 1) = .5788362246256302, (9, 2) = .4985566327609869, (9, 3) = 0.37313069594910674e-1, (9, 4) = .10159768333703968, (9, 5) = -.2329675184040786, (10, 1) = .6853588708527928, (10, 2) = .504526521398875, (10, 3) = 0.20382679676615986e-1, (10, 4) = 0.606567047794537e-1, (10, 5) = -.1557809847294323, (11, 1) = .7934302125147107, (11, 2) = .5077218117791161, (11, 3) = 0.10501648422412073e-1, (11, 4) = 0.3401535257794869e-1, (11, 5) = -0.9702883361504151e-1, (12, 1) = .9024960382686785, (12, 2) = .5093322596657791, (12, 3) = 0.5093151483295916e-2, (12, 4) = 0.17884998462519692e-1, (12, 5) = -0.5623455808801906e-1, (13, 1) = 1.012284543110573, (13, 2) = .5100955651640168, (13, 3) = 0.23195437904716377e-2, (13, 4) = 0.8800007896506692e-2, (13, 5) = -0.3029419520059991e-1, (14, 1) = 1.1224435496090202, (14, 2) = .5104345698316491, (14, 3) = 0.9909285667744439e-3, (14, 4) = 0.4050636647573417e-2, (14, 5) = -0.1517584553753996e-1, (15, 1) = 1.2328614831160174, (15, 2) = .5105756222550529, (15, 3) = 0.395898479049903e-3, (15, 4) = 0.17420870540071946e-2, (15, 5) = -0.70679676150117755e-2, (16, 1) = 1.3434756128476715, (16, 2) = .5106303954198085, (16, 3) = 0.147062675323547e-3, (16, 4) = 0.6987853715227916e-3, (16, 5) = -0.3059943628543717e-2, (17, 1) = 1.4541564025817688, (17, 2) = .5106500758344735, (17, 3) = 0.5016782526067641e-4, (17, 4) = 0.2606614231585554e-3, (17, 5) = -0.12322310129648298e-2, (18, 1) = 1.5648893907808388, (18, 2) = .5106565008224614, (18, 3) = 0.15188983867428313e-4, (18, 4) = 0.8947015334152312e-4, (18, 5) = -0.4615493175592657e-3, (19, 1) = 1.6743138673548472, (19, 2) = .5106582990190938, (19, 3) = 0.3766036798992976e-5, (19, 4) = 0.27659825670281336e-4, (19, 5) = -0.16295043631438081e-3, (20, 1) = 1.780533246301514, (20, 2) = .5106586754129524, (20, 3) = 0.5632933568740209e-6, (20, 4) = 0.6803446974353735e-5, (20, 5) = -0.55451472121262876e-4, (21, 1) = 1.883794455897945, (21, 2) = .5106587096287567, (21, 3) = .0, (21, 4) = .0, (21, 5) = -0.18247231920817762e-4}, datatype = float[8], order = C_order); YP := Matrix(21, 5, {(1, 1) = .0, (1, 2) = .8245101724754578, (1, 3) = -1.0, (1, 4) = -.7109880345825436, (1, 5) = .0, (2, 1) = .14580548143397778, (2, 2) = .6387850483082825, (2, 3) = -.857963238913636, (2, 4) = -.7087869877011237, (2, 5) = 0.3230820571723456e-1, (3, 1) = .2577556073775664, (3, 2) = .4806893773780191, (3, 3) = -.7167515674300292, (3, 4) = -.6944757971749999, (3, 5) = .11720085670609043, (4, 1) = .34110224456170846, (4, 2) = .3499979513587831, (4, 3) = -.5797495081496531, (4, 4) = -.6595302165926753, (4, 5) = .23173000521865406, (5, 1) = .4011617938545637, (5, 2) = .24543411078038904, (5, 3) = -.4513251759894287, (5, 4) = -.6004288125540566, (5, 5) = .3474678380333613, (6, 1) = .4428520778243424, (6, 2) = .16494373679100188, (6, 3) = -.3361497197458259, (6, 4) = -.5193790217421129, (6, 5) = .4358990012808411, (7, 1) = .4705413231882741, (7, 2) = .10579089990103963, (7, 3) = -.23830615973840436, (7, 4) = -.4239568572171149, (7, 5) = .47639845021055693, (8, 1) = .48804935564305746, (8, 2) = 0.6453023961994517e-1, (8, 3) = -.16012402142182885, (8, 4) = -.3249339143694787, (8, 5) = .46288755780560664, (9, 1) = .4985566327609869, (9, 2) = 0.37313069594910674e-1, (9, 3) = -.10159768333703968, (9, 4) = -.2329675184040786, (9, 5) = .4045501164402566, (10, 1) = .504526521398875, (10, 2) = 0.20382679676615986e-1, (10, 3) = -0.606567047794537e-1, (10, 4) = -.1557809847294323, (10, 5) = .32029763938349964, (11, 1) = .5077218117791161, (11, 2) = 0.10501648422412073e-1, (11, 3) = -0.3401535257794869e-1, (11, 4) = -0.9702883361504151e-1, (11, 5) = .23095682422571068, (12, 1) = .5093322596657791, (12, 2) = 0.5093151483295916e-2, (12, 3) = -0.17884998462519692e-1, (12, 4) = -0.5623455808801906e-1, (12, 5) = .15225439766468124, (13, 1) = .5100955651640168, (13, 2) = 0.23195437904716377e-2, (13, 3) = -0.8800007896506692e-2, (13, 4) = -0.3029419520059991e-1, (13, 5) = 0.9199903664262538e-1, (14, 1) = .5104345698316491, (14, 2) = 0.9909285667744439e-3, (14, 3) = -0.4050636647573417e-2, (14, 4) = -0.1517584553753996e-1, (14, 5) = 0.5110208980042368e-1, (15, 1) = .5105756222550529, (15, 2) = 0.395898479049903e-3, (15, 3) = -0.17420870540071946e-2, (15, 4) = -0.70679676150117755e-2, (15, 5) = 0.2614147510937819e-1, (16, 1) = .5106303954198085, (16, 2) = 0.147062675323547e-3, (16, 3) = -0.6987853715227916e-3, (16, 4) = -0.3059943628543717e-2, (16, 5) = 0.12332878924911292e-1, (17, 1) = .5106500758344735, (17, 2) = 0.5016782526067641e-4, (17, 3) = -0.2606614231585554e-3, (17, 4) = -0.12322310129648298e-2, (17, 5) = 0.5375569850887878e-2, (18, 1) = .5106565008224614, (18, 2) = 0.15188983867428313e-4, (18, 3) = -0.8947015334152312e-4, (18, 4) = -0.4615493175592657e-3, (18, 5) = 0.21668208911118933e-2, (19, 1) = .5106582990190938, (19, 2) = 0.3766036798992976e-5, (19, 3) = -0.27659825670281336e-4, (19, 4) = -0.16295043631438081e-3, (19, 5) = 0.818490525638072e-3, (20, 1) = .5106586754129524, (20, 2) = 0.5632933568740209e-6, (20, 3) = -0.6803446974353735e-5, (20, 4) = -0.55451472121262876e-4, (20, 5) = 0.2961995690048103e-3, (21, 1) = .5106587096287567, (21, 2) = .0, (21, 3) = -.0, (21, 4) = -0.18247231920817762e-4, (21, 5) = 0.10312210298376153e-3}, 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(21, {(1) = .0, (2) = .19993050946471785, (3) = .40078377746315347, (4) = .6025727748609847, (5) = .805792602032412, (6) = 1.010942304650061, (7) = 1.2180763336987108, (8) = 1.4270038908463605, (9) = 1.6375902221831404, (10) = 1.8498543724186098, (11) = 2.0633079120179274, (12) = 2.277741391439103, (13) = 2.4931129139047408, (14) = 2.7089887386097495, (15) = 2.9252757828996607, (16) = 3.1419082091550377, (17) = 3.3586565343807853, (18) = 3.5755020065597023, (19) = 3.7897835066856795, (20) = 3.99778821105096, (21) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(21, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.3225282101028832e-8, (1, 4) = .0, (1, 5) = -0.306904489517561e-8, (2, 1) = 0.10246531089716523e-8, (2, 2) = -0.6348273518306401e-9, (2, 3) = 0.5280283045733476e-8, (2, 4) = -0.15460119781465505e-8, (2, 5) = -0.3111972196122568e-8, (3, 1) = 0.14385154241501163e-8, (3, 2) = -0.5659353722457318e-9, (3, 3) = 0.7366067640793483e-8, (3, 4) = -0.205675007440646e-8, (3, 5) = -0.7654892838125813e-9, (4, 1) = 0.13717815683035354e-8, (4, 2) = 0.26028484027032336e-9, (4, 3) = 0.9539892064176174e-8, (4, 4) = 0.24565765082340653e-9, (4, 5) = 0.11311960348109336e-8, (5, 1) = 0.10696619574989934e-8, (5, 2) = 0.20904757573793948e-8, (5, 3) = 0.10897034285849277e-7, (5, 4) = 0.5224442094293148e-8, (5, 5) = -0.982392164165021e-9, (6, 1) = 0.9629629242145679e-9, (6, 2) = 0.4894193344502427e-8, (6, 3) = 0.1017771761404114e-7, (6, 4) = 0.10347525459625882e-7, (6, 5) = -0.7741328730549143e-8, (7, 1) = 0.15636952892286532e-8, (7, 2) = 0.8053337086081324e-8, (7, 3) = 0.6822364946182849e-8, (7, 4) = 0.11785751490900183e-7, (7, 5) = -0.1392691114755755e-7, (8, 1) = 0.31926817803440276e-8, (8, 2) = 0.10509257498152553e-7, (8, 3) = 0.1899720513765137e-8, (8, 4) = 0.760149626720609e-8, (8, 5) = -0.11714120519495598e-7, (9, 1) = 0.57532273237297496e-8, (9, 2) = 0.11421679651998926e-7, (9, 3) = -0.229577357787563e-8, (9, 4) = 0.1716529005384147e-9, (9, 5) = 0.577665988866524e-9, (10, 1) = 0.8784212596184829e-8, (10, 2) = 0.10748645263066323e-7, (10, 3) = -0.39035239946249045e-8, (10, 4) = -0.5427240111839344e-8, (10, 5) = 0.14524777420046239e-7, (11, 1) = 0.11724890676964285e-7, (11, 2) = 0.9216439233216983e-8, (11, 3) = -0.28080368116505204e-8, (11, 4) = -0.5695308336864215e-8, (11, 5) = 0.1854188979169272e-7, (12, 1) = 0.14217506552967113e-7, (12, 2) = 0.7774557393185575e-8, (12, 3) = -0.5359664622676325e-9, (12, 4) = -0.16488517834097276e-8, (12, 5) = 0.9618376961509946e-8, (13, 1) = 0.1621520132087811e-7, (13, 2) = 0.6981599823947951e-8, (13, 3) = 0.11981824806623278e-8, (13, 4) = 0.28334363730160277e-8, (13, 5) = -0.4254474884966903e-8, (14, 1) = 0.17871713577039598e-7, (14, 2) = 0.685266473073148e-8, (14, 3) = 0.16436559065185234e-8, (14, 4) = 0.466176272654239e-8, (14, 5) = -0.12433461653275879e-7, (15, 1) = 0.19390903474282444e-7, (15, 2) = 0.7074088998861169e-8, (15, 3) = 0.11396175692924493e-8, (15, 4) = 0.36232530669465204e-8, (15, 5) = -0.11136510116613177e-7, (16, 1) = 0.20906983042953743e-7, (16, 2) = 0.7336969978980538e-8, (16, 3) = 0.4082968956704066e-9, (16, 4) = 0.14447508719698394e-8, (16, 5) = -0.441131553891032e-8, (17, 1) = 0.2246622279696012e-7, (17, 2) = 0.7494765673871917e-8, (17, 3) = -0.713044618217475e-10, (17, 4) = -0.20531471924327354e-9, (17, 5) = 0.16033357726866474e-8, (18, 1) = 0.24064316105687922e-7, (18, 2) = 0.7543231622589056e-8, (18, 3) = -0.2150775594089281e-9, (18, 4) = -0.7638272588382362e-9, (18, 5) = 0.37681131369972575e-8, (19, 1) = 0.25662794710206375e-7, (19, 2) = 0.7533978157568794e-8, (19, 3) = -0.16368473302264987e-9, (19, 4) = -0.5918687948851731e-9, (19, 5) = 0.28309099745660008e-8, (20, 1) = 0.2721985098806705e-7, (20, 2) = 0.7512291952428403e-8, (20, 3) = -0.6699548282956056e-10, (20, 4) = -0.22995298592357275e-9, (20, 5) = 0.899471197799444e-9, (21, 1) = 0.28733061733775093e-7, (21, 2) = 0.7499038130831793e-8, (21, 3) = .0, (21, 4) = .0, (21, 5) = -0.42801008501024594e-9}, 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[21] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(2.8733061733775093e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 21, [f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[21] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[21] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(21, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(21, 5, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)]'[i] = yout[i], i = 1 .. 5)] 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[21] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(2.8733061733775093e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 21, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[21] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[21] 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(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(21, 5, 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(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(21, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(0..0, {}), (3) = [eta, f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), 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(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [eta = res[1], seq('[f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)]'[i] = res[i+1], i = 1 .. 5)] catch: error  end try end proc

(1)

S1(0)

[eta = 0., f[0](eta) = HFloat(0.0), diff(f[0](eta), eta) = HFloat(0.0), diff(diff(f[0](eta), eta), eta) = HFloat(0.8245101724754578), theta[0](eta) = HFloat(1.0), diff(theta[0](eta), eta) = HFloat(-0.7109880345825436)]

(2)

S1(inf)

[eta = 4.2, f[0](eta) = HFloat(1.8837944558979445), diff(f[0](eta), eta) = HFloat(0.5106587096287566), diff(diff(f[0](eta), eta), eta) = HFloat(0.0), theta[0](eta) = HFloat(0.0), diff(theta[0](eta), eta) = HFloat(-1.824723192081776e-5)]

(3)

NULL

a := 1.88379445589794-.510658709628757*inf

-.260972124

(4)

inf := 10

NULL

equ3 := diff(F[0](xi), `$`(xi, 3))+3*F[0](xi)*(diff(F[0](xi), `$`(xi, 2)))-2*(diff(F[0](xi), xi))^2

diff(diff(diff(F[0](xi), xi), xi), xi)+3*F[0](xi)*(diff(diff(F[0](xi), xi), xi))-2*(diff(F[0](xi), xi))^2

(5)

Bcs11 := F[0](0) = 0, (D(F[0]))(0) = .510618751345326, (D(F[0]))(inf) = 0

F[0](0) = 0, (D(F[0]))(0) = .510618751345326, (D(F[0]))(10) = 0

(6)

S11 := dsolve({Bcs11, equ3}, {F[0](xi)}, type = numeric)

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) 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(23, {(1) = .0, (2) = .43995910756952955, (3) = .8818024979495411, (4) = 1.3270776004308045, (5) = 1.7763484441069568, (6) = 2.229065879136695, (7) = 2.684207128805122, (8) = 3.140817181526158, (9) = 3.5981979167878757, (10) = 4.0559771665647775, (11) = 4.513960436412507, (12) = 4.972035001116527, (13) = 5.430146736418387, (14) = 5.8882754726647875, (15) = 6.346417081862801, (16) = 6.804565947859982, (17) = 7.262708179327477, (18) = 7.720830795175491, (19) = 8.178943307293594, (20) = 8.637079917616942, (21) = 9.095271573062485, (22) = 9.55312550836552, (23) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(23, 3, {(1, 1) = .0, (1, 2) = .510618751345326, (1, 3) = -.5621776449624967, (2, 1) = .17717334220528227, (2, 2) = .3094384103457518, (2, 3) = -.36249778610993466, (3, 1) = .2835457506232679, (3, 2) = .18237603524747753, (3, 3) = -.22215239106093324, (4, 1) = .34609337288531195, (4, 2) = .10528549733875404, (4, 3) = -.1313037143718732, (5, 1) = .38226110558181875, (5, 2) = 0.5986757437392236e-1, (5, 3) = -0.7570052587025905e-1, (6, 1) = .4028817239785081, (6, 2) = 0.3368972489103516e-1, (6, 3) = -0.4293950636267703e-1, (7, 1) = .41451120840782213, (7, 2) = 0.1883373920486776e-1, (7, 3) = -0.24113598781561642e-1, (8, 1) = .4210213973431861, (8, 2) = 0.10487755429959987e-1, (8, 3) = -0.13462644018507802e-1, (9, 1) = .42464905330360847, (9, 2) = 0.5827609213592593e-2, (9, 3) = -0.7492027740321948e-2, (10, 1) = .42666537431298196, (10, 2) = 0.32341752319787276e-2, (10, 3) = -0.41620140393042165e-2, (11, 1) = .42778447655676605, (11, 2) = 0.17934853870152092e-2, (11, 3) = -0.2309891932194095e-2, (12, 1) = .42840502007546755, (12, 2) = 0.9939485823390328e-3, (12, 3) = -0.128132977545255e-2, (13, 1) = .42874885053352857, (13, 2) = 0.5504549692948659e-3, (13, 3) = -0.710585328691742e-3, (14, 1) = .428939188910442, (14, 2) = 0.3045149657496893e-3, (14, 3) = -0.3940128086348384e-3, (15, 1) = .42904440886986595, (15, 2) = 0.16814506760643266e-3, (15, 3) = -0.2184582751864434e-3, (16, 1) = .42910243164507306, (16, 2) = 0.9253589387088047e-4, (16, 3) = -0.12111740438283116e-3, (17, 1) = .4291342856498462, (17, 2) = 0.5061752912533847e-4, (17, 3) = -0.6714895745960031e-4, (18, 1) = .4291516313607923, (18, 2) = 0.27378292595049353e-4, (18, 3) = -0.37228690528137976e-4, (19, 1) = .4291609342033263, (19, 2) = 0.14494226764390213e-4, (19, 3) = -0.20640432198220086e-4, (20, 1) = .42916577833108405, (20, 2) = 0.7350727087129666e-5, (20, 3) = -0.11443117153602244e-4, (21, 1) = .42916815033963046, (21, 2) = 0.3389993912843161e-5, (21, 3) = -0.6343627852532419e-5, (22, 1) = .4291691510446365, (22, 2) = 0.11954976052799754e-5, (22, 3) = -0.35181854688677843e-5, (23, 1) = .4291693927115069, (23, 2) = .0, (23, 3) = -0.1978965807811915e-5}, datatype = float[8], order = C_order); YP := Matrix(23, 3, {(1, 1) = .510618751345326, (1, 2) = -.5621776449624967, (1, 3) = .5214630184509197, (2, 1) = .3094384103457518, (2, 2) = -.36249778610993466, (2, 3) = .3841790925159498, (3, 1) = .18237603524747753, (3, 2) = -.22215239106093324, (3, 3) = .25549313589355654, (4, 1) = .10528549733875404, (4, 2) = -.1313037143718732, (4, 3) = .15850010803773118, (5, 1) = 0.5986757437392236e-1, (5, 2) = -0.7570052587025905e-1, (5, 3) = 0.9398035305970513e-1, (6, 1) = 0.3368972489103516e-1, (6, 2) = -0.4293950636267703e-1, (6, 3) = 0.5416862217701158e-1, (7, 1) = 0.1883373920486776e-1, (7, 2) = -0.24113598781561642e-1, (7, 3) = 0.3069549037489346e-1, (8, 1) = 0.10487755429959987e-1, (8, 2) = -0.13462644018507802e-1, (8, 3) = 0.17224169617735433e-1, (9, 1) = 0.5827609213592593e-2, (9, 2) = -0.7492027740321948e-2, (9, 3) = 0.9612369520048963e-2, (10, 1) = 0.32341752319787276e-2, (10, 2) = -0.41620140393042165e-2, (10, 3) = 0.5348281612789148e-2, (11, 1) = 0.17934853870152092e-2, (11, 2) = -0.2309891932194095e-2, (11, 3) = 0.29708409130159183e-2, (12, 1) = 0.9939485823390328e-3, (12, 2) = -0.128132977545255e-2, (12, 3) = 0.16487601920967994e-2, (13, 1) = 0.5504549692948659e-3, (13, 2) = -0.710585328691742e-3, (13, 3) = 0.9145939299941647e-3, (14, 1) = 0.3045149657496893e-3, (14, 2) = -0.3940128086348384e-3, (14, 3) = 0.5072080623971895e-3, (15, 1) = 0.16814506760643266e-3, (15, 2) = -0.2184582751864434e-3, (15, 3) = 0.2812414501478151e-3, (16, 1) = 0.9253589387088047e-4, (16, 2) = -0.12111740438283116e-3, (16, 3) = 0.15593244398894642e-3, (17, 1) = 0.5061752912533847e-4, (17, 2) = -0.6714895745960031e-4, (17, 3) = 0.8645288394318198e-4, (18, 1) = 0.27378292595049353e-4, (18, 2) = -0.37228690528137976e-4, (18, 3) = 0.47931758962540315e-4, (19, 1) = 0.14494226764390213e-4, (19, 2) = -0.20640432198220086e-4, (19, 3) = 0.26574621658864638e-4, (20, 1) = 0.7350727087129666e-5, (20, 2) = -0.11443117153602244e-4, (20, 3) = 0.14733090905655878e-4, (21, 1) = 0.3389993912843161e-5, (21, 2) = -0.6343627852532419e-5, (21, 3) = 0.8167472079860358e-5, (22, 1) = 0.11954976052799754e-5, (22, 2) = -0.35181854688677843e-5, (22, 3) = 0.4529692871103739e-5, (23, 1) = .0, (23, 2) = -0.1978965807811915e-5, (23, 3) = 0.25479346618064288e-5}, 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(23, {(1) = .0, (2) = .43995910756952955, (3) = .8818024979495411, (4) = 1.3270776004308045, (5) = 1.7763484441069568, (6) = 2.229065879136695, (7) = 2.684207128805122, (8) = 3.140817181526158, (9) = 3.5981979167878757, (10) = 4.0559771665647775, (11) = 4.513960436412507, (12) = 4.972035001116527, (13) = 5.430146736418387, (14) = 5.8882754726647875, (15) = 6.346417081862801, (16) = 6.804565947859982, (17) = 7.262708179327477, (18) = 7.720830795175491, (19) = 8.178943307293594, (20) = 8.637079917616942, (21) = 9.095271573062485, (22) = 9.55312550836552, (23) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(23, 3, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.8443585204955963e-7, (2, 1) = 0.8072589267659636e-7, (2, 2) = -0.13040637822613006e-6, (2, 3) = 0.15281918615445138e-6, (3, 1) = 0.39989750781142555e-7, (3, 2) = -0.11177533439806323e-6, (3, 3) = 0.1352441905854288e-6, (4, 1) = -0.20600025919174704e-7, (4, 2) = -0.3663790652273445e-7, (4, 3) = 0.3961571511177524e-7, (5, 1) = -0.49196188461498834e-7, (5, 2) = 0.5492226766989574e-8, (5, 3) = -0.1811804632665225e-7, (6, 1) = -0.5176128689580457e-7, (6, 2) = 0.10746044825613138e-7, (6, 3) = -0.24261078473670985e-7, (7, 1) = -0.4605856538385761e-7, (7, 2) = 0.2347487092667642e-8, (7, 3) = -0.10120809582466025e-7, (8, 1) = -0.4167885627474688e-7, (8, 2) = -0.50636120787681426e-8, (8, 3) = 0.2710185594404049e-8, (9, 1) = -0.4055994520021322e-7, (9, 2) = -0.7884739911451825e-8, (9, 3) = 0.8563777546638327e-8, (10, 1) = -0.41605931611661884e-7, (10, 2) = -0.7347948086520706e-8, (10, 3) = 0.908101908275086e-8, (11, 1) = -0.43422115575092884e-7, (11, 2) = -0.5397359425838763e-8, (11, 3) = 0.7106596371627789e-8, (12, 1) = -0.45148718532454525e-7, (12, 2) = -0.33200029720200515e-8, (12, 3) = 0.45977051212970705e-8, (13, 1) = -0.4644624587319399e-7, (13, 2) = -0.16812844515373377e-8, (13, 3) = 0.2476976139544679e-8, (14, 1) = -0.4728162048888603e-7, (14, 2) = -0.597980012160218e-9, (14, 3) = 0.10035287537696905e-8, (15, 1) = -0.4774964466124897e-7, (15, 2) = 0.1516792967540915e-10, (15, 3) = 0.1216447480458187e-9, (16, 1) = -0.4797098512847073e-7, (16, 2) = 0.2984480082832177e-9, (16, 3) = -0.32609332485037004e-9, (17, 1) = -0.4804804671209328e-7, (17, 2) = 0.3798012127372219e-9, (17, 3) = -0.497031217110049e-9, (18, 1) = -0.4805324175520197e-7, (18, 2) = 0.3535479474474593e-9, (18, 3) = -0.5125103792466736e-9, (19, 1) = -0.48031643002679316e-7, (19, 2) = 0.28054921031195175e-9, (19, 3) = -0.4535792419789312e-9, (20, 1) = -0.4800808931165307e-7, (20, 2) = 0.19581304022615792e-9, (20, 3) = -0.3686139862436758e-9, (21, 1) = -0.4799424116835274e-7, (21, 2) = 0.11696392107492342e-9, (21, 3) = -0.2833008145543955e-9, (22, 1) = -0.4799400195331907e-7, (22, 2) = 0.51123446927522176e-10, (22, 3) = -0.20919618553471444e-9, (23, 1) = -0.4800625077534693e-7, (23, 2) = .0, (23, 3) = -0.15020239214744807e-9}, 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[23] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(1.5281918615445138e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [3, 23, [F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(3, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(23, 3, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(3, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(23, 3, X, Y, outpoint, yout, L, V) end if; [xi = outpoint, seq('[F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)]'[i] = yout[i], i = 1 .. 3)] 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[23] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(1.5281918615445138e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [3, 23, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] 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(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(23, 3, 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(3, {(1) = 0., (2) = 0., (3) = 0.}); `dsolve/numeric/hermite`(23, 3, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 3)] end proc, (2) = Array(0..0, {}), (3) = [xi, F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)], (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(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [xi = res[1], seq('[F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)]'[i] = res[i+1], i = 1 .. 3)] catch: error  end try end proc

(7)

S11(0)

[xi = 0., F[0](xi) = HFloat(0.0), diff(F[0](xi), xi) = HFloat(0.5106187513453263), diff(diff(F[0](xi), xi), xi) = HFloat(-0.562177644962497)]

(8)

S11(inf)

[xi = 10., F[0](xi) = HFloat(0.42916939271150717), diff(F[0](xi), xi) = HFloat(0.0), diff(diff(F[0](xi), xi), xi) = HFloat(-1.9789658078119164e-6)]

(9)

NULL

NULL

inf := 4.2

equ4 := diff(f[1](eta), `$`(eta, 3))+theta[1](eta) = 0

equ5 := diff(theta[1](eta), `$`(eta, 2))+(3*1.88379445589794)*(diff(theta[1](eta), eta))+(3*(-0.182472319208178e-4))*f[1](eta) = 0

Bcs2 := f[1](0) = 0, (D(f[1]))(0) = 0, theta[1](0) = 0, theta[1](inf) = 0, (D(D(f[1])))(inf) = -.562177644962497

S2 := dsolve({Bcs2, equ4, equ5}, {f[1](eta), theta[1](eta)}, type = numeric)

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) 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(11, {(1) = .0, (2) = .4116634332886109, (3) = .8886010476858462, (4) = 1.3528488149076092, (5) = 1.8045807366238487, (6) = 2.241555102796764, (7) = 2.6625695592004965, (8) = 3.0672725690885674, (9) = 3.4556665515316527, (10) = 3.831324258983187, (11) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(11, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -.5619986895834216, (1, 4) = .0, (1, 5) = 0.335774149965343e-3, (2, 1) = -0.4762032358997575e-1, (2, 2) = -.23135669488800123, (2, 3) = -.5620136602440209, (2, 4) = 0.53584183105081106e-4, (2, 5) = 0.3259167905984578e-4, (3, 1) = -.22188452637683598, (3, 2) = -.49940857560864915, (3, 3) = -.5620409665524415, (3, 4) = 0.58646668768565734e-4, (3, 5) = 0.7416150484543588e-6, (4, 1) = -.5143020373634434, (4, 2) = -.7603411477852857, (4, 3) = -.5620680774630706, (4, 4) = 0.5782030426624352e-4, (4, 5) = -0.3686352453447587e-5, (5, 1) = -.9151215778516861, (5, 2) = -1.0142510703826526, (5, 3) = -.5620937045204393, (5, 4) = 0.55371378860239725e-4, (5, 5) = -0.72839758029738255e-5, (6, 1) = -1.41198899414111, (6, 2) = -1.2598767815850975, (6, 3) = -.5621170728942686, (6, 4) = 0.51263362070545665e-4, (6, 5) = -0.11687120529486582e-4, (7, 1) = -1.9922344707360793, (7, 2) = -1.4965405780807717, (7, 3) = -.5621374727450006, (7, 4) = 0.4527873193435496e-4, (7, 5) = -0.16902962326608247e-4, (8, 1) = -2.643924136984444, (8, 2) = -1.7240428108976953, (8, 3) = -.5621542573727711, (8, 4) = 0.3726965687176117e-4, (8, 5) = -0.22825657629343497e-4, (9, 1) = -3.3559327840238864, (9, 2) = -1.9423827145168133, (9, 3) = -.5621668522332793, (9, 4) = 0.2716422553072306e-4, (9, 5) = -0.29348255430226227e-4, (10, 1) = -4.125270167459166, (10, 2) = -2.1535666676671648, (10, 3) = -.5621748236492027, (10, 4) = 0.14831645690104376e-4, (10, 5) = -0.3643841995320963e-4, (11, 1) = -4.957443956702882, (11, 2) = -2.3608275753757364, (11, 3) = -.562177644962497, (11, 4) = .0, (11, 5) = -0.4414396637606905e-4}, datatype = float[8], order = C_order); YP := Matrix(11, 5, {(1, 1) = .0, (1, 2) = -.5619986895834216, (1, 3) = -.0, (1, 4) = 0.335774149965343e-3, (1, 5) = -0.18975884465184773e-2, (2, 1) = -.23135669488800123, (2, 2) = -.5620136602440209, (2, 3) = -0.53584183105081106e-4, (2, 4) = 0.3259167905984578e-4, (2, 5) = -0.18679489023996156e-3, (3, 1) = -.49940857560864915, (3, 2) = -.5620409665524415, (3, 3) = -0.58646668768565734e-4, (3, 4) = 0.7416150484543588e-6, (3, 5) = -0.16337486187065928e-4, (4, 1) = -.7603411477852857, (4, 2) = -.5620680774630706, (4, 3) = -0.5782030426624352e-4, (4, 4) = -0.3686352453447587e-5, (4, 5) = -0.732077471409808e-5, (5, 1) = -1.0142510703826526, (5, 2) = -.5620937045204393, (5, 3) = -0.55371378860239725e-4, (5, 4) = -0.72839758029738255e-5, (5, 5) = -0.893076729232743e-5, (6, 1) = -1.2598767815850975, (6, 2) = -.5621170728942686, (6, 3) = -0.51263362070545665e-4, (6, 4) = -0.11687120529486582e-4, (6, 5) = -0.11246273353589229e-4, (7, 1) = -1.4965405780807717, (7, 2) = -.5621374727450006, (7, 3) = -0.4527873193435496e-4, (7, 4) = -0.16902962326608247e-4, (7, 5) = -0.13533173117094628e-4, (8, 1) = -1.7240428108976953, (8, 2) = -.5621542573727711, (8, 3) = -0.3726965687176117e-4, (8, 4) = -0.22825657629343497e-4, (8, 5) = -0.1573634882918884e-4, (9, 1) = -1.9423827145168133, (9, 2) = -.5621668522332793, (9, 3) = -0.2716422553072306e-4, (9, 4) = -0.29348255430226227e-4, (9, 5) = -0.17851208835849183e-4, (10, 1) = -2.1535666676671648, (10, 2) = -.5621748236492027, (10, 3) = -0.14831645690104376e-4, (10, 4) = -0.3643841995320963e-4, (10, 5) = -0.1989680395508565e-4, (11, 1) = -2.3608275753757364, (11, 2) = -.562177644962497, (11, 3) = -.0, (11, 4) = -0.4414396637606905e-4, (11, 5) = -0.2190441144981183e-4}, 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(11, {(1) = .0, (2) = .4116634332886109, (3) = .8886010476858462, (4) = 1.3528488149076092, (5) = 1.8045807366238487, (6) = 2.241555102796764, (7) = 2.6625695592004965, (8) = 3.0672725690885674, (9) = 3.4556665515316527, (10) = 3.831324258983187, (11) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(11, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.35508604778067024e-15, (1, 4) = .0, (1, 5) = 0.15397753328418554e-14, (2, 1) = 0.2558116197637096e-10, (2, 2) = -0.14456757081707498e-9, (2, 3) = 0.817011120093731e-9, (2, 4) = 0.4617236684306891e-8, (2, 5) = -0.2609377331174807e-7, (3, 1) = -0.9457936005633856e-11, (3, 2) = 0.5345381823058202e-10, (3, 3) = -0.30207991081338217e-9, (3, 4) = -0.1707174526030626e-8, (3, 5) = 0.9647899354096491e-8, (4, 1) = 0.2020346996825016e-11, (4, 2) = -0.11415519234215377e-10, (4, 3) = 0.6451847526201498e-10, (4, 4) = 0.3646134887612831e-9, (4, 5) = -0.2060569086207772e-8, (5, 1) = -0.17646929046515701e-12, (5, 2) = 0.10093169744755152e-11, (5, 3) = -0.5699389218375125e-11, (5, 4) = -0.3221591809328718e-10, (5, 5) = 0.18206604502968212e-9, (6, 1) = 0.8757302096159674e-14, (6, 2) = -0.3799530988879617e-13, (6, 3) = 0.2292287437287893e-12, (6, 4) = 0.12945323288954797e-11, (6, 5) = -0.731435866077949e-11, (7, 1) = -0.9110226200220738e-15, (7, 2) = 0.25567726327308368e-13, (7, 3) = -0.12993934244362953e-12, (7, 4) = -0.7335757077118738e-12, (7, 5) = 0.4147257410839353e-11, (8, 1) = 0.26358911697616852e-14, (8, 2) = 0.3882634055360638e-14, (8, 3) = -0.9480934215017551e-14, (8, 4) = -0.55231163150641485e-13, (8, 5) = 0.31367270612471335e-12, (9, 1) = 0.7629602722383346e-14, (9, 2) = 0.4396554488606655e-14, (9, 3) = -0.15992210754706523e-14, (9, 4) = -0.1230013855036495e-13, (9, 5) = 0.7105291182052132e-13, (10, 1) = 0.1485070353377911e-13, (10, 2) = 0.33969966675655985e-14, (10, 3) = -0.6675463903849193e-15, (10, 4) = -0.14924562287319862e-14, (10, 5) = 0.9974730177955179e-14, (11, 1) = 0.38908323477587536e-14, (11, 2) = 0.32750628566257692e-14, (11, 3) = .0, (11, 4) = .0, (11, 5) = 0.15404022343639915e-14}, 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[11] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.609377331174807e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 11, [f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[11] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[11] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(11, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(11, 5, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)]'[i] = yout[i], i = 1 .. 5)] 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[11] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.609377331174807e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 11, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[11] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[11] 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(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(11, 5, 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(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(11, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(0..0, {}), (3) = [eta, f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), 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(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [eta = res[1], seq('[f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)]'[i] = res[i+1], i = 1 .. 5)] catch: error  end try end proc

(10)

S2(0)

[eta = 0., f[1](eta) = HFloat(0.0), diff(f[1](eta), eta) = HFloat(0.0), diff(diff(f[1](eta), eta), eta) = HFloat(-0.5619986895834218), theta[1](eta) = HFloat(0.0), diff(theta[1](eta), eta) = HFloat(3.3577414996534315e-4)]

(11)

S2(inf)

[eta = 4.2, f[1](eta) = HFloat(-4.95744395670288), diff(f[1](eta), eta) = HFloat(-2.3608275753757355), diff(diff(f[1](eta), eta), eta) = HFloat(-0.5621776449624968), theta[1](eta) = HFloat(0.0), diff(theta[1](eta), eta) = HFloat(-4.414396637606903e-5)]

(12)

"b:="

inf := 10

equ6 := diff(F[1](xi), `$`(xi, 3))-(4*.510618751345326)*(diff(F[1](xi), xi))+(3*(-.562177644962497))*F[1](0) = 0

diff(diff(diff(F[1](xi), xi), xi), xi)-2.042475005*(diff(F[1](xi), xi))-1.686532935*F[1](0) = 0

(13)

Bcs21 := F[1](0) = a, (D(F[1]))(0) = .510658709628757, (D(F[1]))(inf) = 0

F[1](0) = -.260972124, (D(F[1]))(0) = .510658709628757, (D(F[1]))(10) = 0

(14)

S21 := dsolve({Bcs21, equ6}, {F[1](xi)}, type = numeric)

Error, (in fproc) unable to store 'HFloat(1.0430076505022892)+1.686532935*F[1](0)' when datatype=float[8]

 

NULL

NULL


 

Download kuikennnnnn.mw
 

NULL

restart

Digits := 10

with(ODETools)

with(student)

with(plots)

inf := 4.2

NULL

equ1 := diff(f[0](eta), `$`(eta, 3))+theta[0](eta) = 0

equ2 := diff(theta[0](eta), `$`(eta, 2))+3*f[0](eta)*(diff(theta[0](eta), eta)) = 0

Bcs1 := f[0](0) = 0, (D(f[0]))(0) = 0, theta[0](0) = 1, theta[0](inf) = 0, (D(D(f[0])))(inf) = 0

S1 := dsolve({Bcs1, equ1, equ2}, {f[0](eta), theta[0](eta)}, type = numeric)

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) 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(21, {(1) = .0, (2) = .19993050946471785, (3) = .40078377746315347, (4) = .6025727748609847, (5) = .805792602032412, (6) = 1.010942304650061, (7) = 1.2180763336987108, (8) = 1.4270038908463605, (9) = 1.6375902221831404, (10) = 1.8498543724186098, (11) = 2.0633079120179274, (12) = 2.277741391439103, (13) = 2.4931129139047408, (14) = 2.7089887386097495, (15) = 2.9252757828996607, (16) = 3.1419082091550377, (17) = 3.3586565343807853, (18) = 3.5755020065597023, (19) = 3.7897835066856795, (20) = 3.99778821105096, (21) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(21, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .8245101724754578, (1, 4) = 1.0, (1, 5) = -.7109880345825436, (2, 1) = 0.15194130384185354e-1, (2, 2) = .14580548143397778, (2, 3) = .6387850483082825, (2, 4) = .857963238913636, (2, 5) = -.7087869877011237, (3, 1) = 0.5625387147295941e-1, (3, 2) = .2577556073775664, (3, 3) = .4806893773780191, (3, 4) = .7167515674300292, (3, 5) = -.6944757971749999, (4, 1) = .11711872046127954, (4, 2) = .34110224456170846, (4, 3) = .3499979513587831, (4, 4) = .5797495081496531, (4, 5) = -.6595302165926753, (5, 1) = .19289982468547776, (5, 2) = .4011617938545637, (5, 3) = .24543411078038904, (5, 4) = .4513251759894287, (5, 5) = -.6004288125540566, (6, 1) = .2797565188640971, (6, 2) = .4428520778243424, (6, 3) = .16494373679100188, (6, 4) = .3361497197458259, (6, 5) = -.5193790217421129, (7, 1) = .37456519619918616, (7, 2) = .4705413231882741, (7, 3) = .10579089990103963, (7, 4) = .23830615973840436, (7, 5) = -.4239568572171149, (8, 1) = .4748530263492926, (8, 2) = .48804935564305746, (8, 3) = 0.6453023961994517e-1, (8, 4) = .16012402142182885, (8, 5) = -.3249339143694787, (9, 1) = .5788362246256302, (9, 2) = .4985566327609869, (9, 3) = 0.37313069594910674e-1, (9, 4) = .10159768333703968, (9, 5) = -.2329675184040786, (10, 1) = .6853588708527928, (10, 2) = .504526521398875, (10, 3) = 0.20382679676615986e-1, (10, 4) = 0.606567047794537e-1, (10, 5) = -.1557809847294323, (11, 1) = .7934302125147107, (11, 2) = .5077218117791161, (11, 3) = 0.10501648422412073e-1, (11, 4) = 0.3401535257794869e-1, (11, 5) = -0.9702883361504151e-1, (12, 1) = .9024960382686785, (12, 2) = .5093322596657791, (12, 3) = 0.5093151483295916e-2, (12, 4) = 0.17884998462519692e-1, (12, 5) = -0.5623455808801906e-1, (13, 1) = 1.012284543110573, (13, 2) = .5100955651640168, (13, 3) = 0.23195437904716377e-2, (13, 4) = 0.8800007896506692e-2, (13, 5) = -0.3029419520059991e-1, (14, 1) = 1.1224435496090202, (14, 2) = .5104345698316491, (14, 3) = 0.9909285667744439e-3, (14, 4) = 0.4050636647573417e-2, (14, 5) = -0.1517584553753996e-1, (15, 1) = 1.2328614831160174, (15, 2) = .5105756222550529, (15, 3) = 0.395898479049903e-3, (15, 4) = 0.17420870540071946e-2, (15, 5) = -0.70679676150117755e-2, (16, 1) = 1.3434756128476715, (16, 2) = .5106303954198085, (16, 3) = 0.147062675323547e-3, (16, 4) = 0.6987853715227916e-3, (16, 5) = -0.3059943628543717e-2, (17, 1) = 1.4541564025817688, (17, 2) = .5106500758344735, (17, 3) = 0.5016782526067641e-4, (17, 4) = 0.2606614231585554e-3, (17, 5) = -0.12322310129648298e-2, (18, 1) = 1.5648893907808388, (18, 2) = .5106565008224614, (18, 3) = 0.15188983867428313e-4, (18, 4) = 0.8947015334152312e-4, (18, 5) = -0.4615493175592657e-3, (19, 1) = 1.6743138673548472, (19, 2) = .5106582990190938, (19, 3) = 0.3766036798992976e-5, (19, 4) = 0.27659825670281336e-4, (19, 5) = -0.16295043631438081e-3, (20, 1) = 1.780533246301514, (20, 2) = .5106586754129524, (20, 3) = 0.5632933568740209e-6, (20, 4) = 0.6803446974353735e-5, (20, 5) = -0.55451472121262876e-4, (21, 1) = 1.883794455897945, (21, 2) = .5106587096287567, (21, 3) = .0, (21, 4) = .0, (21, 5) = -0.18247231920817762e-4}, datatype = float[8], order = C_order); YP := Matrix(21, 5, {(1, 1) = .0, (1, 2) = .8245101724754578, (1, 3) = -1.0, (1, 4) = -.7109880345825436, (1, 5) = .0, (2, 1) = .14580548143397778, (2, 2) = .6387850483082825, (2, 3) = -.857963238913636, (2, 4) = -.7087869877011237, (2, 5) = 0.3230820571723456e-1, (3, 1) = .2577556073775664, (3, 2) = .4806893773780191, (3, 3) = -.7167515674300292, (3, 4) = -.6944757971749999, (3, 5) = .11720085670609043, (4, 1) = .34110224456170846, (4, 2) = .3499979513587831, (4, 3) = -.5797495081496531, (4, 4) = -.6595302165926753, (4, 5) = .23173000521865406, (5, 1) = .4011617938545637, (5, 2) = .24543411078038904, (5, 3) = -.4513251759894287, (5, 4) = -.6004288125540566, (5, 5) = .3474678380333613, (6, 1) = .4428520778243424, (6, 2) = .16494373679100188, (6, 3) = -.3361497197458259, (6, 4) = -.5193790217421129, (6, 5) = .4358990012808411, (7, 1) = .4705413231882741, (7, 2) = .10579089990103963, (7, 3) = -.23830615973840436, (7, 4) = -.4239568572171149, (7, 5) = .47639845021055693, (8, 1) = .48804935564305746, (8, 2) = 0.6453023961994517e-1, (8, 3) = -.16012402142182885, (8, 4) = -.3249339143694787, (8, 5) = .46288755780560664, (9, 1) = .4985566327609869, (9, 2) = 0.37313069594910674e-1, (9, 3) = -.10159768333703968, (9, 4) = -.2329675184040786, (9, 5) = .4045501164402566, (10, 1) = .504526521398875, (10, 2) = 0.20382679676615986e-1, (10, 3) = -0.606567047794537e-1, (10, 4) = -.1557809847294323, (10, 5) = .32029763938349964, (11, 1) = .5077218117791161, (11, 2) = 0.10501648422412073e-1, (11, 3) = -0.3401535257794869e-1, (11, 4) = -0.9702883361504151e-1, (11, 5) = .23095682422571068, (12, 1) = .5093322596657791, (12, 2) = 0.5093151483295916e-2, (12, 3) = -0.17884998462519692e-1, (12, 4) = -0.5623455808801906e-1, (12, 5) = .15225439766468124, (13, 1) = .5100955651640168, (13, 2) = 0.23195437904716377e-2, (13, 3) = -0.8800007896506692e-2, (13, 4) = -0.3029419520059991e-1, (13, 5) = 0.9199903664262538e-1, (14, 1) = .5104345698316491, (14, 2) = 0.9909285667744439e-3, (14, 3) = -0.4050636647573417e-2, (14, 4) = -0.1517584553753996e-1, (14, 5) = 0.5110208980042368e-1, (15, 1) = .5105756222550529, (15, 2) = 0.395898479049903e-3, (15, 3) = -0.17420870540071946e-2, (15, 4) = -0.70679676150117755e-2, (15, 5) = 0.2614147510937819e-1, (16, 1) = .5106303954198085, (16, 2) = 0.147062675323547e-3, (16, 3) = -0.6987853715227916e-3, (16, 4) = -0.3059943628543717e-2, (16, 5) = 0.12332878924911292e-1, (17, 1) = .5106500758344735, (17, 2) = 0.5016782526067641e-4, (17, 3) = -0.2606614231585554e-3, (17, 4) = -0.12322310129648298e-2, (17, 5) = 0.5375569850887878e-2, (18, 1) = .5106565008224614, (18, 2) = 0.15188983867428313e-4, (18, 3) = -0.8947015334152312e-4, (18, 4) = -0.4615493175592657e-3, (18, 5) = 0.21668208911118933e-2, (19, 1) = .5106582990190938, (19, 2) = 0.3766036798992976e-5, (19, 3) = -0.27659825670281336e-4, (19, 4) = -0.16295043631438081e-3, (19, 5) = 0.818490525638072e-3, (20, 1) = .5106586754129524, (20, 2) = 0.5632933568740209e-6, (20, 3) = -0.6803446974353735e-5, (20, 4) = -0.55451472121262876e-4, (20, 5) = 0.2961995690048103e-3, (21, 1) = .5106587096287567, (21, 2) = .0, (21, 3) = -.0, (21, 4) = -0.18247231920817762e-4, (21, 5) = 0.10312210298376153e-3}, 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(21, {(1) = .0, (2) = .19993050946471785, (3) = .40078377746315347, (4) = .6025727748609847, (5) = .805792602032412, (6) = 1.010942304650061, (7) = 1.2180763336987108, (8) = 1.4270038908463605, (9) = 1.6375902221831404, (10) = 1.8498543724186098, (11) = 2.0633079120179274, (12) = 2.277741391439103, (13) = 2.4931129139047408, (14) = 2.7089887386097495, (15) = 2.9252757828996607, (16) = 3.1419082091550377, (17) = 3.3586565343807853, (18) = 3.5755020065597023, (19) = 3.7897835066856795, (20) = 3.99778821105096, (21) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(21, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.3225282101028832e-8, (1, 4) = .0, (1, 5) = -0.306904489517561e-8, (2, 1) = 0.10246531089716523e-8, (2, 2) = -0.6348273518306401e-9, (2, 3) = 0.5280283045733476e-8, (2, 4) = -0.15460119781465505e-8, (2, 5) = -0.3111972196122568e-8, (3, 1) = 0.14385154241501163e-8, (3, 2) = -0.5659353722457318e-9, (3, 3) = 0.7366067640793483e-8, (3, 4) = -0.205675007440646e-8, (3, 5) = -0.7654892838125813e-9, (4, 1) = 0.13717815683035354e-8, (4, 2) = 0.26028484027032336e-9, (4, 3) = 0.9539892064176174e-8, (4, 4) = 0.24565765082340653e-9, (4, 5) = 0.11311960348109336e-8, (5, 1) = 0.10696619574989934e-8, (5, 2) = 0.20904757573793948e-8, (5, 3) = 0.10897034285849277e-7, (5, 4) = 0.5224442094293148e-8, (5, 5) = -0.982392164165021e-9, (6, 1) = 0.9629629242145679e-9, (6, 2) = 0.4894193344502427e-8, (6, 3) = 0.1017771761404114e-7, (6, 4) = 0.10347525459625882e-7, (6, 5) = -0.7741328730549143e-8, (7, 1) = 0.15636952892286532e-8, (7, 2) = 0.8053337086081324e-8, (7, 3) = 0.6822364946182849e-8, (7, 4) = 0.11785751490900183e-7, (7, 5) = -0.1392691114755755e-7, (8, 1) = 0.31926817803440276e-8, (8, 2) = 0.10509257498152553e-7, (8, 3) = 0.1899720513765137e-8, (8, 4) = 0.760149626720609e-8, (8, 5) = -0.11714120519495598e-7, (9, 1) = 0.57532273237297496e-8, (9, 2) = 0.11421679651998926e-7, (9, 3) = -0.229577357787563e-8, (9, 4) = 0.1716529005384147e-9, (9, 5) = 0.577665988866524e-9, (10, 1) = 0.8784212596184829e-8, (10, 2) = 0.10748645263066323e-7, (10, 3) = -0.39035239946249045e-8, (10, 4) = -0.5427240111839344e-8, (10, 5) = 0.14524777420046239e-7, (11, 1) = 0.11724890676964285e-7, (11, 2) = 0.9216439233216983e-8, (11, 3) = -0.28080368116505204e-8, (11, 4) = -0.5695308336864215e-8, (11, 5) = 0.1854188979169272e-7, (12, 1) = 0.14217506552967113e-7, (12, 2) = 0.7774557393185575e-8, (12, 3) = -0.5359664622676325e-9, (12, 4) = -0.16488517834097276e-8, (12, 5) = 0.9618376961509946e-8, (13, 1) = 0.1621520132087811e-7, (13, 2) = 0.6981599823947951e-8, (13, 3) = 0.11981824806623278e-8, (13, 4) = 0.28334363730160277e-8, (13, 5) = -0.4254474884966903e-8, (14, 1) = 0.17871713577039598e-7, (14, 2) = 0.685266473073148e-8, (14, 3) = 0.16436559065185234e-8, (14, 4) = 0.466176272654239e-8, (14, 5) = -0.12433461653275879e-7, (15, 1) = 0.19390903474282444e-7, (15, 2) = 0.7074088998861169e-8, (15, 3) = 0.11396175692924493e-8, (15, 4) = 0.36232530669465204e-8, (15, 5) = -0.11136510116613177e-7, (16, 1) = 0.20906983042953743e-7, (16, 2) = 0.7336969978980538e-8, (16, 3) = 0.4082968956704066e-9, (16, 4) = 0.14447508719698394e-8, (16, 5) = -0.441131553891032e-8, (17, 1) = 0.2246622279696012e-7, (17, 2) = 0.7494765673871917e-8, (17, 3) = -0.713044618217475e-10, (17, 4) = -0.20531471924327354e-9, (17, 5) = 0.16033357726866474e-8, (18, 1) = 0.24064316105687922e-7, (18, 2) = 0.7543231622589056e-8, (18, 3) = -0.2150775594089281e-9, (18, 4) = -0.7638272588382362e-9, (18, 5) = 0.37681131369972575e-8, (19, 1) = 0.25662794710206375e-7, (19, 2) = 0.7533978157568794e-8, (19, 3) = -0.16368473302264987e-9, (19, 4) = -0.5918687948851731e-9, (19, 5) = 0.28309099745660008e-8, (20, 1) = 0.2721985098806705e-7, (20, 2) = 0.7512291952428403e-8, (20, 3) = -0.6699548282956056e-10, (20, 4) = -0.22995298592357275e-9, (20, 5) = 0.899471197799444e-9, (21, 1) = 0.28733061733775093e-7, (21, 2) = 0.7499038130831793e-8, (21, 3) = .0, (21, 4) = .0, (21, 5) = -0.42801008501024594e-9}, 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[21] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(2.8733061733775093e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 21, [f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[21] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[21] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(21, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(21, 5, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)]'[i] = yout[i], i = 1 .. 5)] 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[21] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(2.8733061733775093e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 21, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[21] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[21] 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(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(21, 5, 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(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(21, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(0..0, {}), (3) = [eta, f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), 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(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [eta = res[1], seq('[f[0](eta), diff(f[0](eta), eta), diff(diff(f[0](eta), eta), eta), theta[0](eta), diff(theta[0](eta), eta)]'[i] = res[i+1], i = 1 .. 5)] catch: error  end try end proc

(1)

S1(0)

[eta = 0., f[0](eta) = HFloat(0.0), diff(f[0](eta), eta) = HFloat(0.0), diff(diff(f[0](eta), eta), eta) = HFloat(0.8245101724754578), theta[0](eta) = HFloat(1.0), diff(theta[0](eta), eta) = HFloat(-0.7109880345825436)]

(2)

S1(inf)

[eta = 4.2, f[0](eta) = HFloat(1.8837944558979445), diff(f[0](eta), eta) = HFloat(0.5106587096287566), diff(diff(f[0](eta), eta), eta) = HFloat(0.0), theta[0](eta) = HFloat(0.0), diff(theta[0](eta), eta) = HFloat(-1.824723192081776e-5)]

(3)

NULL

a := 1.88379445589794-.510658709628757*inf

-.260972124

(4)

inf := 10

NULL

equ3 := diff(F[0](xi), `$`(xi, 3))+3*F[0](xi)*(diff(F[0](xi), `$`(xi, 2)))-2*(diff(F[0](xi), xi))^2

diff(diff(diff(F[0](xi), xi), xi), xi)+3*F[0](xi)*(diff(diff(F[0](xi), xi), xi))-2*(diff(F[0](xi), xi))^2

(5)

Bcs11 := F[0](0) = 0, (D(F[0]))(0) = .510618751345326, (D(F[0]))(inf) = 0

F[0](0) = 0, (D(F[0]))(0) = .510618751345326, (D(F[0]))(10) = 0

(6)

S11 := dsolve({Bcs11, equ3}, {F[0](xi)}, type = numeric)

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) 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(23, {(1) = .0, (2) = .43995910756952955, (3) = .8818024979495411, (4) = 1.3270776004308045, (5) = 1.7763484441069568, (6) = 2.229065879136695, (7) = 2.684207128805122, (8) = 3.140817181526158, (9) = 3.5981979167878757, (10) = 4.0559771665647775, (11) = 4.513960436412507, (12) = 4.972035001116527, (13) = 5.430146736418387, (14) = 5.8882754726647875, (15) = 6.346417081862801, (16) = 6.804565947859982, (17) = 7.262708179327477, (18) = 7.720830795175491, (19) = 8.178943307293594, (20) = 8.637079917616942, (21) = 9.095271573062485, (22) = 9.55312550836552, (23) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(23, 3, {(1, 1) = .0, (1, 2) = .510618751345326, (1, 3) = -.5621776449624967, (2, 1) = .17717334220528227, (2, 2) = .3094384103457518, (2, 3) = -.36249778610993466, (3, 1) = .2835457506232679, (3, 2) = .18237603524747753, (3, 3) = -.22215239106093324, (4, 1) = .34609337288531195, (4, 2) = .10528549733875404, (4, 3) = -.1313037143718732, (5, 1) = .38226110558181875, (5, 2) = 0.5986757437392236e-1, (5, 3) = -0.7570052587025905e-1, (6, 1) = .4028817239785081, (6, 2) = 0.3368972489103516e-1, (6, 3) = -0.4293950636267703e-1, (7, 1) = .41451120840782213, (7, 2) = 0.1883373920486776e-1, (7, 3) = -0.24113598781561642e-1, (8, 1) = .4210213973431861, (8, 2) = 0.10487755429959987e-1, (8, 3) = -0.13462644018507802e-1, (9, 1) = .42464905330360847, (9, 2) = 0.5827609213592593e-2, (9, 3) = -0.7492027740321948e-2, (10, 1) = .42666537431298196, (10, 2) = 0.32341752319787276e-2, (10, 3) = -0.41620140393042165e-2, (11, 1) = .42778447655676605, (11, 2) = 0.17934853870152092e-2, (11, 3) = -0.2309891932194095e-2, (12, 1) = .42840502007546755, (12, 2) = 0.9939485823390328e-3, (12, 3) = -0.128132977545255e-2, (13, 1) = .42874885053352857, (13, 2) = 0.5504549692948659e-3, (13, 3) = -0.710585328691742e-3, (14, 1) = .428939188910442, (14, 2) = 0.3045149657496893e-3, (14, 3) = -0.3940128086348384e-3, (15, 1) = .42904440886986595, (15, 2) = 0.16814506760643266e-3, (15, 3) = -0.2184582751864434e-3, (16, 1) = .42910243164507306, (16, 2) = 0.9253589387088047e-4, (16, 3) = -0.12111740438283116e-3, (17, 1) = .4291342856498462, (17, 2) = 0.5061752912533847e-4, (17, 3) = -0.6714895745960031e-4, (18, 1) = .4291516313607923, (18, 2) = 0.27378292595049353e-4, (18, 3) = -0.37228690528137976e-4, (19, 1) = .4291609342033263, (19, 2) = 0.14494226764390213e-4, (19, 3) = -0.20640432198220086e-4, (20, 1) = .42916577833108405, (20, 2) = 0.7350727087129666e-5, (20, 3) = -0.11443117153602244e-4, (21, 1) = .42916815033963046, (21, 2) = 0.3389993912843161e-5, (21, 3) = -0.6343627852532419e-5, (22, 1) = .4291691510446365, (22, 2) = 0.11954976052799754e-5, (22, 3) = -0.35181854688677843e-5, (23, 1) = .4291693927115069, (23, 2) = .0, (23, 3) = -0.1978965807811915e-5}, datatype = float[8], order = C_order); YP := Matrix(23, 3, {(1, 1) = .510618751345326, (1, 2) = -.5621776449624967, (1, 3) = .5214630184509197, (2, 1) = .3094384103457518, (2, 2) = -.36249778610993466, (2, 3) = .3841790925159498, (3, 1) = .18237603524747753, (3, 2) = -.22215239106093324, (3, 3) = .25549313589355654, (4, 1) = .10528549733875404, (4, 2) = -.1313037143718732, (4, 3) = .15850010803773118, (5, 1) = 0.5986757437392236e-1, (5, 2) = -0.7570052587025905e-1, (5, 3) = 0.9398035305970513e-1, (6, 1) = 0.3368972489103516e-1, (6, 2) = -0.4293950636267703e-1, (6, 3) = 0.5416862217701158e-1, (7, 1) = 0.1883373920486776e-1, (7, 2) = -0.24113598781561642e-1, (7, 3) = 0.3069549037489346e-1, (8, 1) = 0.10487755429959987e-1, (8, 2) = -0.13462644018507802e-1, (8, 3) = 0.17224169617735433e-1, (9, 1) = 0.5827609213592593e-2, (9, 2) = -0.7492027740321948e-2, (9, 3) = 0.9612369520048963e-2, (10, 1) = 0.32341752319787276e-2, (10, 2) = -0.41620140393042165e-2, (10, 3) = 0.5348281612789148e-2, (11, 1) = 0.17934853870152092e-2, (11, 2) = -0.2309891932194095e-2, (11, 3) = 0.29708409130159183e-2, (12, 1) = 0.9939485823390328e-3, (12, 2) = -0.128132977545255e-2, (12, 3) = 0.16487601920967994e-2, (13, 1) = 0.5504549692948659e-3, (13, 2) = -0.710585328691742e-3, (13, 3) = 0.9145939299941647e-3, (14, 1) = 0.3045149657496893e-3, (14, 2) = -0.3940128086348384e-3, (14, 3) = 0.5072080623971895e-3, (15, 1) = 0.16814506760643266e-3, (15, 2) = -0.2184582751864434e-3, (15, 3) = 0.2812414501478151e-3, (16, 1) = 0.9253589387088047e-4, (16, 2) = -0.12111740438283116e-3, (16, 3) = 0.15593244398894642e-3, (17, 1) = 0.5061752912533847e-4, (17, 2) = -0.6714895745960031e-4, (17, 3) = 0.8645288394318198e-4, (18, 1) = 0.27378292595049353e-4, (18, 2) = -0.37228690528137976e-4, (18, 3) = 0.47931758962540315e-4, (19, 1) = 0.14494226764390213e-4, (19, 2) = -0.20640432198220086e-4, (19, 3) = 0.26574621658864638e-4, (20, 1) = 0.7350727087129666e-5, (20, 2) = -0.11443117153602244e-4, (20, 3) = 0.14733090905655878e-4, (21, 1) = 0.3389993912843161e-5, (21, 2) = -0.6343627852532419e-5, (21, 3) = 0.8167472079860358e-5, (22, 1) = 0.11954976052799754e-5, (22, 2) = -0.35181854688677843e-5, (22, 3) = 0.4529692871103739e-5, (23, 1) = .0, (23, 2) = -0.1978965807811915e-5, (23, 3) = 0.25479346618064288e-5}, 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(23, {(1) = .0, (2) = .43995910756952955, (3) = .8818024979495411, (4) = 1.3270776004308045, (5) = 1.7763484441069568, (6) = 2.229065879136695, (7) = 2.684207128805122, (8) = 3.140817181526158, (9) = 3.5981979167878757, (10) = 4.0559771665647775, (11) = 4.513960436412507, (12) = 4.972035001116527, (13) = 5.430146736418387, (14) = 5.8882754726647875, (15) = 6.346417081862801, (16) = 6.804565947859982, (17) = 7.262708179327477, (18) = 7.720830795175491, (19) = 8.178943307293594, (20) = 8.637079917616942, (21) = 9.095271573062485, (22) = 9.55312550836552, (23) = 10.0}, datatype = float[8], order = C_order); Y := Matrix(23, 3, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.8443585204955963e-7, (2, 1) = 0.8072589267659636e-7, (2, 2) = -0.13040637822613006e-6, (2, 3) = 0.15281918615445138e-6, (3, 1) = 0.39989750781142555e-7, (3, 2) = -0.11177533439806323e-6, (3, 3) = 0.1352441905854288e-6, (4, 1) = -0.20600025919174704e-7, (4, 2) = -0.3663790652273445e-7, (4, 3) = 0.3961571511177524e-7, (5, 1) = -0.49196188461498834e-7, (5, 2) = 0.5492226766989574e-8, (5, 3) = -0.1811804632665225e-7, (6, 1) = -0.5176128689580457e-7, (6, 2) = 0.10746044825613138e-7, (6, 3) = -0.24261078473670985e-7, (7, 1) = -0.4605856538385761e-7, (7, 2) = 0.2347487092667642e-8, (7, 3) = -0.10120809582466025e-7, (8, 1) = -0.4167885627474688e-7, (8, 2) = -0.50636120787681426e-8, (8, 3) = 0.2710185594404049e-8, (9, 1) = -0.4055994520021322e-7, (9, 2) = -0.7884739911451825e-8, (9, 3) = 0.8563777546638327e-8, (10, 1) = -0.41605931611661884e-7, (10, 2) = -0.7347948086520706e-8, (10, 3) = 0.908101908275086e-8, (11, 1) = -0.43422115575092884e-7, (11, 2) = -0.5397359425838763e-8, (11, 3) = 0.7106596371627789e-8, (12, 1) = -0.45148718532454525e-7, (12, 2) = -0.33200029720200515e-8, (12, 3) = 0.45977051212970705e-8, (13, 1) = -0.4644624587319399e-7, (13, 2) = -0.16812844515373377e-8, (13, 3) = 0.2476976139544679e-8, (14, 1) = -0.4728162048888603e-7, (14, 2) = -0.597980012160218e-9, (14, 3) = 0.10035287537696905e-8, (15, 1) = -0.4774964466124897e-7, (15, 2) = 0.1516792967540915e-10, (15, 3) = 0.1216447480458187e-9, (16, 1) = -0.4797098512847073e-7, (16, 2) = 0.2984480082832177e-9, (16, 3) = -0.32609332485037004e-9, (17, 1) = -0.4804804671209328e-7, (17, 2) = 0.3798012127372219e-9, (17, 3) = -0.497031217110049e-9, (18, 1) = -0.4805324175520197e-7, (18, 2) = 0.3535479474474593e-9, (18, 3) = -0.5125103792466736e-9, (19, 1) = -0.48031643002679316e-7, (19, 2) = 0.28054921031195175e-9, (19, 3) = -0.4535792419789312e-9, (20, 1) = -0.4800808931165307e-7, (20, 2) = 0.19581304022615792e-9, (20, 3) = -0.3686139862436758e-9, (21, 1) = -0.4799424116835274e-7, (21, 2) = 0.11696392107492342e-9, (21, 3) = -0.2833008145543955e-9, (22, 1) = -0.4799400195331907e-7, (22, 2) = 0.51123446927522176e-10, (22, 3) = -0.20919618553471444e-9, (23, 1) = -0.4800625077534693e-7, (23, 2) = .0, (23, 3) = -0.15020239214744807e-9}, 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[23] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(1.5281918615445138e-7) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [3, 23, [F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(3, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(23, 3, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(3, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(23, 3, X, Y, outpoint, yout, L, V) end if; [xi = outpoint, seq('[F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)]'[i] = yout[i], i = 1 .. 3)] 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[23] elif outpoint = "order" then return 6 elif outpoint = "error" then return HFloat(1.5281918615445138e-7) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [3, 23, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[23] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[23] 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(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(23, 3, 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(3, {(1) = 0., (2) = 0., (3) = 0.}); `dsolve/numeric/hermite`(23, 3, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 3)] end proc, (2) = Array(0..0, {}), (3) = [xi, F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)], (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(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [xi = res[1], seq('[F[0](xi), diff(F[0](xi), xi), diff(diff(F[0](xi), xi), xi)]'[i] = res[i+1], i = 1 .. 3)] catch: error  end try end proc

(7)

S11(0)

[xi = 0., F[0](xi) = HFloat(0.0), diff(F[0](xi), xi) = HFloat(0.5106187513453263), diff(diff(F[0](xi), xi), xi) = HFloat(-0.562177644962497)]

(8)

S11(inf)

[xi = 10., F[0](xi) = HFloat(0.42916939271150717), diff(F[0](xi), xi) = HFloat(0.0), diff(diff(F[0](xi), xi), xi) = HFloat(-1.9789658078119164e-6)]

(9)

NULL

NULL

inf := 4.2

equ4 := diff(f[1](eta), `$`(eta, 3))+theta[1](eta) = 0

equ5 := diff(theta[1](eta), `$`(eta, 2))+(3*1.88379445589794)*(diff(theta[1](eta), eta))+(3*(-0.182472319208178e-4))*f[1](eta) = 0

Bcs2 := f[1](0) = 0, (D(f[1]))(0) = 0, theta[1](0) = 0, theta[1](inf) = 0, (D(D(f[1])))(inf) = -.562177644962497

S2 := dsolve({Bcs2, equ4, equ5}, {f[1](eta), theta[1](eta)}, type = numeric)

proc (x_bvp) local res, data, solnproc, _ndsol, outpoint, i; option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; _EnvDSNumericSaveDigits := Digits; Digits := 15; if _EnvInFsolve = true then outpoint := evalf[_EnvDSNumericSaveDigits](x_bvp) else outpoint := evalf(x_bvp) 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(11, {(1) = .0, (2) = .4116634332886109, (3) = .8886010476858462, (4) = 1.3528488149076092, (5) = 1.8045807366238487, (6) = 2.241555102796764, (7) = 2.6625695592004965, (8) = 3.0672725690885674, (9) = 3.4556665515316527, (10) = 3.831324258983187, (11) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(11, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = -.5619986895834216, (1, 4) = .0, (1, 5) = 0.335774149965343e-3, (2, 1) = -0.4762032358997575e-1, (2, 2) = -.23135669488800123, (2, 3) = -.5620136602440209, (2, 4) = 0.53584183105081106e-4, (2, 5) = 0.3259167905984578e-4, (3, 1) = -.22188452637683598, (3, 2) = -.49940857560864915, (3, 3) = -.5620409665524415, (3, 4) = 0.58646668768565734e-4, (3, 5) = 0.7416150484543588e-6, (4, 1) = -.5143020373634434, (4, 2) = -.7603411477852857, (4, 3) = -.5620680774630706, (4, 4) = 0.5782030426624352e-4, (4, 5) = -0.3686352453447587e-5, (5, 1) = -.9151215778516861, (5, 2) = -1.0142510703826526, (5, 3) = -.5620937045204393, (5, 4) = 0.55371378860239725e-4, (5, 5) = -0.72839758029738255e-5, (6, 1) = -1.41198899414111, (6, 2) = -1.2598767815850975, (6, 3) = -.5621170728942686, (6, 4) = 0.51263362070545665e-4, (6, 5) = -0.11687120529486582e-4, (7, 1) = -1.9922344707360793, (7, 2) = -1.4965405780807717, (7, 3) = -.5621374727450006, (7, 4) = 0.4527873193435496e-4, (7, 5) = -0.16902962326608247e-4, (8, 1) = -2.643924136984444, (8, 2) = -1.7240428108976953, (8, 3) = -.5621542573727711, (8, 4) = 0.3726965687176117e-4, (8, 5) = -0.22825657629343497e-4, (9, 1) = -3.3559327840238864, (9, 2) = -1.9423827145168133, (9, 3) = -.5621668522332793, (9, 4) = 0.2716422553072306e-4, (9, 5) = -0.29348255430226227e-4, (10, 1) = -4.125270167459166, (10, 2) = -2.1535666676671648, (10, 3) = -.5621748236492027, (10, 4) = 0.14831645690104376e-4, (10, 5) = -0.3643841995320963e-4, (11, 1) = -4.957443956702882, (11, 2) = -2.3608275753757364, (11, 3) = -.562177644962497, (11, 4) = .0, (11, 5) = -0.4414396637606905e-4}, datatype = float[8], order = C_order); YP := Matrix(11, 5, {(1, 1) = .0, (1, 2) = -.5619986895834216, (1, 3) = -.0, (1, 4) = 0.335774149965343e-3, (1, 5) = -0.18975884465184773e-2, (2, 1) = -.23135669488800123, (2, 2) = -.5620136602440209, (2, 3) = -0.53584183105081106e-4, (2, 4) = 0.3259167905984578e-4, (2, 5) = -0.18679489023996156e-3, (3, 1) = -.49940857560864915, (3, 2) = -.5620409665524415, (3, 3) = -0.58646668768565734e-4, (3, 4) = 0.7416150484543588e-6, (3, 5) = -0.16337486187065928e-4, (4, 1) = -.7603411477852857, (4, 2) = -.5620680774630706, (4, 3) = -0.5782030426624352e-4, (4, 4) = -0.3686352453447587e-5, (4, 5) = -0.732077471409808e-5, (5, 1) = -1.0142510703826526, (5, 2) = -.5620937045204393, (5, 3) = -0.55371378860239725e-4, (5, 4) = -0.72839758029738255e-5, (5, 5) = -0.893076729232743e-5, (6, 1) = -1.2598767815850975, (6, 2) = -.5621170728942686, (6, 3) = -0.51263362070545665e-4, (6, 4) = -0.11687120529486582e-4, (6, 5) = -0.11246273353589229e-4, (7, 1) = -1.4965405780807717, (7, 2) = -.5621374727450006, (7, 3) = -0.4527873193435496e-4, (7, 4) = -0.16902962326608247e-4, (7, 5) = -0.13533173117094628e-4, (8, 1) = -1.7240428108976953, (8, 2) = -.5621542573727711, (8, 3) = -0.3726965687176117e-4, (8, 4) = -0.22825657629343497e-4, (8, 5) = -0.1573634882918884e-4, (9, 1) = -1.9423827145168133, (9, 2) = -.5621668522332793, (9, 3) = -0.2716422553072306e-4, (9, 4) = -0.29348255430226227e-4, (9, 5) = -0.17851208835849183e-4, (10, 1) = -2.1535666676671648, (10, 2) = -.5621748236492027, (10, 3) = -0.14831645690104376e-4, (10, 4) = -0.3643841995320963e-4, (10, 5) = -0.1989680395508565e-4, (11, 1) = -2.3608275753757364, (11, 2) = -.562177644962497, (11, 3) = -.0, (11, 4) = -0.4414396637606905e-4, (11, 5) = -0.2190441144981183e-4}, 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(11, {(1) = .0, (2) = .4116634332886109, (3) = .8886010476858462, (4) = 1.3528488149076092, (5) = 1.8045807366238487, (6) = 2.241555102796764, (7) = 2.6625695592004965, (8) = 3.0672725690885674, (9) = 3.4556665515316527, (10) = 3.831324258983187, (11) = 4.2}, datatype = float[8], order = C_order); Y := Matrix(11, 5, {(1, 1) = .0, (1, 2) = .0, (1, 3) = 0.35508604778067024e-15, (1, 4) = .0, (1, 5) = 0.15397753328418554e-14, (2, 1) = 0.2558116197637096e-10, (2, 2) = -0.14456757081707498e-9, (2, 3) = 0.817011120093731e-9, (2, 4) = 0.4617236684306891e-8, (2, 5) = -0.2609377331174807e-7, (3, 1) = -0.9457936005633856e-11, (3, 2) = 0.5345381823058202e-10, (3, 3) = -0.30207991081338217e-9, (3, 4) = -0.1707174526030626e-8, (3, 5) = 0.9647899354096491e-8, (4, 1) = 0.2020346996825016e-11, (4, 2) = -0.11415519234215377e-10, (4, 3) = 0.6451847526201498e-10, (4, 4) = 0.3646134887612831e-9, (4, 5) = -0.2060569086207772e-8, (5, 1) = -0.17646929046515701e-12, (5, 2) = 0.10093169744755152e-11, (5, 3) = -0.5699389218375125e-11, (5, 4) = -0.3221591809328718e-10, (5, 5) = 0.18206604502968212e-9, (6, 1) = 0.8757302096159674e-14, (6, 2) = -0.3799530988879617e-13, (6, 3) = 0.2292287437287893e-12, (6, 4) = 0.12945323288954797e-11, (6, 5) = -0.731435866077949e-11, (7, 1) = -0.9110226200220738e-15, (7, 2) = 0.25567726327308368e-13, (7, 3) = -0.12993934244362953e-12, (7, 4) = -0.7335757077118738e-12, (7, 5) = 0.4147257410839353e-11, (8, 1) = 0.26358911697616852e-14, (8, 2) = 0.3882634055360638e-14, (8, 3) = -0.9480934215017551e-14, (8, 4) = -0.55231163150641485e-13, (8, 5) = 0.31367270612471335e-12, (9, 1) = 0.7629602722383346e-14, (9, 2) = 0.4396554488606655e-14, (9, 3) = -0.15992210754706523e-14, (9, 4) = -0.1230013855036495e-13, (9, 5) = 0.7105291182052132e-13, (10, 1) = 0.1485070353377911e-13, (10, 2) = 0.33969966675655985e-14, (10, 3) = -0.6675463903849193e-15, (10, 4) = -0.14924562287319862e-14, (10, 5) = 0.9974730177955179e-14, (11, 1) = 0.38908323477587536e-14, (11, 2) = 0.32750628566257692e-14, (11, 3) = .0, (11, 4) = .0, (11, 5) = 0.15404022343639915e-14}, 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[11] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.609377331174807e-8) elif outpoint = "errorproc" then error "this is already the error procedure" elif outpoint = "rawdata" then return [5, 11, [f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)], X, Y] else return ('procname')(x_bvp) end if end if; if outpoint < X[1] or X[11] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[11] end if; V := array([1 = 4, 2 = 0]); if Digits <= trunc(evalhf(Digits)) then L := Vector(4, 'datatype' = 'float'[8]); yout := Vector(5, 'datatype' = 'float'[8]); evalhf(`dsolve/numeric/lagrange`(11, 5, X, Y, outpoint, var(yout), var(L), var(V))) else L := Vector(4, 'datatype' = 'sfloat'); yout := Vector(5, 'datatype' = 'sfloat'); `dsolve/numeric/lagrange`(11, 5, X, Y, outpoint, yout, L, V) end if; [eta = outpoint, seq('[f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)]'[i] = yout[i], i = 1 .. 5)] 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[11] elif outpoint = "order" then return 8 elif outpoint = "error" then return HFloat(2.609377331174807e-8) elif outpoint = "errorproc" then return eval(errproc) elif outpoint = "rawdata" then return [5, 11, "depnames", X, Y, YP] else error "non-numeric value" end if end if; if outpoint < X[1] or X[11] < outpoint then error "solution is only defined in the range %1..%2", X[1], X[11] 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(5, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0}, datatype = float[8]); evalhf(`dsolve/numeric/hermite`(11, 5, 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(5, {(1) = 0., (2) = 0., (3) = 0., (4) = 0., (5) = 0.}); `dsolve/numeric/hermite`(11, 5, X, Y, YP, outpoint, yout, L, V) end if; [outpoint, seq(yout[i], i = 1 .. 5)] end proc, (2) = Array(0..0, {}), (3) = [eta, f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), 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(x_bvp) elif outpoint = "sysvars" then return data[3] elif procname <> unknown then return ('procname')(x_bvp) else _ndsol := pointto(data[2][0]); return ('_ndsol')(x_bvp) end if end if; try res := solnproc(outpoint); [eta = res[1], seq('[f[1](eta), diff(f[1](eta), eta), diff(diff(f[1](eta), eta), eta), theta[1](eta), diff(theta[1](eta), eta)]'[i] = res[i+1], i = 1 .. 5)] catch: error  end try end proc

(10)

S2(0)

[eta = 0., f[1](eta) = HFloat(0.0), diff(f[1](eta), eta) = HFloat(0.0), diff(diff(f[1](eta), eta), eta) = HFloat(-0.5619986895834218), theta[1](eta) = HFloat(0.0), diff(theta[1](eta), eta) = HFloat(3.3577414996534315e-4)]

(11)

S2(inf)

[eta = 4.2, f[1](eta) = HFloat(-4.95744395670288), diff(f[1](eta), eta) = HFloat(-2.3608275753757355), diff(diff(f[1](eta), eta), eta) = HFloat(-0.5621776449624968), theta[1](eta) = HFloat(0.0), diff(theta[1](eta), eta) = HFloat(-4.414396637606903e-5)]

(12)

"b:="

inf := 10

equ6 := diff(F[1](xi), `$`(xi, 3))-(4*.510618751345326)*(diff(F[1](xi), xi))+(3*(-.562177644962497))*F[1](0) = 0

diff(diff(diff(F[1](xi), xi), xi), xi)-2.042475005*(diff(F[1](xi), xi))-1.686532935*F[1](0) = 0

(13)

Bcs21 := F[1](0) = a, (D(F[1]))(0) = .510658709628757, (D(F[1]))(inf) = 0

F[1](0) = -.260972124, (D(F[1]))(0) = .510658709628757, (D(F[1]))(10) = 0

(14)

S21 := dsolve({Bcs21, equ6}, {F[1](xi)}, type = numeric)

Error, (in fproc) unable to store 'HFloat(1.0430076505022892)+1.686532935*F[1](0)' when datatype=float[8]

 

 

 

 

Help me, please!

If i have boundary conditions with D(psi), i have no problem. But if i have condition with psi(infinity) (which i need), Maple says "too few boundary conditions". Maybe i make stupid mistakes, but i don't see.

 

restart;
assume(r, nonnegative);
ic_Re := `&psi;Re`(0) = 0, (D(`&psi;Re`))(0) = 0;
ic_Im := `&psi;Im`(0) = 0, (D(`&psi;Im`))(0) = 0;
V0 := 2.5; ERe := 1.5; EIm := 1.2; `&hbar;` := 6.582; mu := 938.27*(1/2); Q0 := 1.5; Rq := 4.5; Rv := 2.5;
Q := proc (r) options operator, arrow; -Q0*exp(-r/Rq) end proc;
V := proc (r) options operator, arrow; -V0*exp(-r/Rv) end proc;
`Eqn_&psi;Re` := -`&hbar;`^2*(diff(`&psi;Re`(r), r, r)+2*(diff(`&psi;Re`(r), r))/r)/(2*mu)-ERe*`&psi;Re`(r)+V(r)+EIm*`&psi;Re`(r) = Q(r);
`Eqn_&psi;Im` := -`&hbar;`^2*(diff(`&psi;Im`(r), r, r)+2*(diff(`&psi;Im`(r), r))/r)/(2*mu)-EIm*`&psi;Re`(r)-ERe*`&psi;Im`(r) = 0;
F := dsolve({ic_Im, ic_Re, `Eqn_&psi;Im`, `Eqn_&psi;Re`}, numeric);
plots[odeplot](F, [r, `&psi;Re`(r)], r = 0 .. 20, numpoints = 500);

plots[odeplot](F, [r, `&psi;Re`(r)], r = 0 .. 20, numpoints = 500);

restart;
assume(r, nonnegative);
ic_Re := `&psi;Re`(0) = 0, `&psi;Re`(infinity) = 0;
ic_Im := `&psi;Im`(0) = 0, `&psi;Im`(infinity) = 0;
V0 := 2.5; ERe := 1.5; EIm := 1.2; `&hbar;` := 6.582; mu := 938.27*(1/2); Q0 := 1.5; Rq := 4.5; Rv := 2.5;
Q := proc (r) options operator, arrow; -Q0*exp(-r/Rq) end proc;
V := proc (r) options operator, arrow; -V0*exp(-r/Rv) end proc;
`Eqn_&psi;Re` := -`&hbar;`^2*(diff(`&psi;Re`(r), r, r)+2*(diff(`&psi;Re`(r), r))/r)/(2*mu)-ERe*`&psi;Re`(r)+V(r)+EIm*`&psi;Re`(r) = Q(r);
`Eqn_&psi;Im` := -`&hbar;`^2*(diff(`&psi;Im`(r), r, r)+2*(diff(`&psi;Im`(r), r))/r)/(2*mu)-EIm*`&psi;Re`(r)-ERe*`&psi;Im`(r) = 0;
F := dsolve({ic_Im, ic_Re, `Eqn_&psi;Im`, `Eqn_&psi;Re`}, numeric);
Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 5, got 4

Hi

may every one help to me for dsolve this differentia1l equation?

error:

Error, (in dsolve/numeric/bvp) singularity encountered

Turbulent2-kw.mw

dsol1 := dsolve({diff(theta(eta), eta, eta)-3*Omega(eta)*(F(eta)*(diff(theta(eta), eta))-theta(eta)*(diff(F(eta), eta)))/(2*K(eta))+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(theta(eta), eta)) = 0, diff(F(eta), eta, eta, eta)+Omega(eta)*(3*F(eta)*(diff(F(eta), eta, eta))-(diff(F(eta), eta))^2)/(2*K(eta))+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(F(eta), eta, eta))+Omega(eta)/K(eta) = 0, diff(K(eta), eta, eta)+Omega(eta)*(1.5*F(eta)*(diff(K(eta), eta))-K(eta)*(diff(F(eta), eta)))/K(eta)+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(K(eta), eta))+(diff(F(eta), eta, eta))^2-Omega(eta)^2 = 0, diff(Omega(eta), eta, eta)+Omega(eta)*(3*F(eta)*(diff(Omega(eta), eta))+Omega(eta)*(diff(F(eta), eta)))/(2*K(eta))+((diff(K(eta), eta))/K(eta)-(diff(Omega(eta), eta))/Omega(eta))*(diff(Omega(eta), eta))+Omega(eta)*(diff(F(eta), eta, eta))^2/K(eta)-Omega(eta)^3/K(eta) = 0, F(0) = 0, K(0) = 0, Omega(0) = 0., theta(0) = 1, theta(1) = 0, (D(F))(0) = 0, (D(K))(1) = 0, (D(Omega))(1) = 0, ((D@@2)(F))(1) = 0}, numeric, method = bvp[middefer], output = listprocedure, initmesh = 512)

Error, (in dsolve/numeric/bvp) singularity encountered

 

NULL

plots[odeplot](dsol1, [(D(F))(eta), eta])

Error, (in plots/odeplot) input is not a valid dsolve/numeric solution

 

``



Download Turbulent2-kw.mw

 

 

 

Hello all..

Im sharena and i am solving ODE BVP by using maple. i used this command to solved the equation..

 

However, i dont know which method this programm solved my ODE. Is it RK45 method??

restart;
Digits := 5;
with(ODETools);
with(student);
with(plots);
inf := 5;
with(LinearAlgebra);
equ1 := (1+2*n)*f(eta)*(diff(theta(eta), eta))/(1+3*n)-(diff(theta(eta), `$`(eta, 2))) = 0;
equ2 := ((1+n)*(diff(f(eta), eta))^2/(1+3*n)-(1+2*n)*f(eta)*(diff(f(eta), eta, eta))/(1+3*n))/Bo+(diff(f(eta), `$`(eta, 3)))^n-theta(eta) = 0;
Bcs := f(0) = 0, (D(f))(0) = 0, (D(f))(inf) = 0, theta(0) = 1, theta(inf) = 0;
Bo := 1; n := 2;
SolP1 := dsolve({Bcs, equ1, equ2}, numeric);
Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system
SolP1(0);
SolP1(0)

> restart:with(plots):blt:=7:

 

 

> lambda:=2:m:=3:s:=1:

> Eq1:=(diff(f(eta),eta,eta,eta))+(f(eta)*(diff(f(eta),eta,eta)))-((diff(f(eta),eta))^2)+lambda*(((f(eta)*(diff(f(eta),eta,eta,eta))))-2*(diff(f(eta),eta))*(diff(f(eta),eta,eta,eta))^2)-(M/(1+m^2))*((diff(f(eta),eta)+ms))=0;

 

>

> Eq2:=(diff(h(eta),eta,eta))+(f(eta)*(diff(h(eta),eta)))-((diff(f(eta),eta))*(h(eta)))+lambda*(((f(eta)*(diff(h(eta),eta,eta,eta))))+(h(eta)*(diff(f(eta),eta,eta,eta)))+(diff(f(eta),eta,eta))*(diff(h(eta),eta))-2*(diff(f(eta),eta))*(diff(h(eta),eta,eta))+(M/(1+m^2)))*(m*(diff(f(eta),eta)-h))=0;

 

>

> Eq3:=((f(eta))*(diff(theta(eta),eta)))+Pr*((diff(theta(eta),eta,eta)))=0;

 

>

> bcs1 := f(0) = 0, (D(f))(0) = 1, (h)(0) = 0, (theta)(0) = 1, (D(f))(blt) = 0,  h(blt) = 0, theta(blt) = 0, D(D(f))(blt) = 0, (D(h))(blt)=0;

 

>

> L := [1,2,3];

 

> for k to 3 do R := dsolve(eval({Eq1, Eq2, Eq3, bcs1}, M = L[k]), [f(eta),h(eta),theta(eta)], numeric, maxmesh=10000, output = listprocedure);;Y || k := rhs(R[3]); YA || k := rhs(R[6]);YB || k := rhs(R[5]);YC || k := rhs(R[4]);YD || k := rhs(R[7]);end do:

>

 

>

>

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

hi

please help me for dsolve differential equations...after much time dont answer!!!

thanks..

dsolve.mw

Digits := 15; SYS := [.16783*h1(theta)-0.96238e-3*(diff(h1(theta), theta, theta))+0.61603e-1*(diff(h2(theta), theta))+0.14870e-4*(diff(h2(theta), theta, theta, theta))-.23703*h3(theta)-0.84431e-3*(diff(h3(theta), theta, theta))+3.4919*10^(-7)*(diff(h1(theta), theta, theta, theta, theta)) = 0, 2.3940*h2(theta)-.35329*(diff(h2(theta), theta, theta))-0.68260e-1*(diff(h1(theta), theta))-0.16526e-4*(diff(h1(theta), theta, theta, theta))+3.0808*(diff(h3(theta), theta))-0.17833e-2*(diff(h3(theta), theta, theta, theta)) = 0, 9.4813*10^(-7)/((1.+1.5802*10^(-8)*h3(theta))*ln(10.+1.5802*10^(-7)*h3(theta))^2)-3.1867/((1.-0.26556e-1*h3(theta))*ln(10.-.26556*h3(theta))^2)-7.6530/((1.-0.31888e-1*h3(theta))*ln(10.-.31888*h3(theta))^2)-4.2551/((1.-0.35459e-1*h3(theta))*ln(10.-.35459*h3(theta))^2)-9.0315/((1.-0.37632e-1*h3(theta))*ln(10.-.37632*h3(theta))^2)-4.6587/((1.-0.38822e-1*h3(theta))*ln(10.-.38822*h3(theta))^2)-9.4520/((1.-0.39384e-1*h3(theta))*ln(10.-.39384*h3(theta))^2)+0.74999e-1/((1.+0.12500e-2*h3(theta))*ln(10.+0.12500e-1*h3(theta))^2)-.69143/((1.-0.28810e-2*h3(theta))*ln(10.-0.28810e-1*h3(theta))^2)-.12945/(1.-0.38836e-1*h3(theta))^4-0.38260e-1/(1.-0.11478e-1*h3(theta))^4-0.24826e-1/(1.-0.37240e-2*h3(theta))^4+0.74712e-3*(diff(h3(theta), theta, theta, theta, theta))+2.6337*10^(-8)/(1.+1.5802*10^(-8)*h3(theta))^4-0.27242e-1*(diff(h3(theta), theta, theta))-3.0707*(diff(h2(theta), theta))+0.17833e-2*(diff(h2(theta), theta, theta, theta))-.23618*h1(theta)-0.84126e-3*(diff(h1(theta), theta, theta))-0.89222e-1/(1.-0.26767e-1*h3(theta))^4-.21340/(1.-0.32010e-1*h3(theta))^4-.13154/(1.-0.19732e-1*h3(theta))^4-0.88519e-1/(1.-0.26556e-1*h3(theta))^4-4.7454/((1.-0.39545e-1*h3(theta))*ln(10.-.39545*h3(theta))^2)-0.36390e-1/(1.-0.10917e-1*h3(theta))^4-1.3100/((1.-0.10917e-1*h3(theta))*ln(10.-.10917*h3(theta))^2)-.89374/((1.-0.37240e-2*h3(theta))*ln(10.-0.37240e-1*h3(theta))^2)-1.3773/((1.-0.11478e-1*h3(theta))*ln(10.-.11478*h3(theta))^2)-.11820/(1.-0.35459e-1*h3(theta))^4-.26259/(1.-0.39388e-1*h3(theta))^4-4.7356/((1.-0.19732e-1*h3(theta))*ln(10.-.19732*h3(theta))^2)+28.586*h3(theta)-.21258/(1.-0.31888e-1*h3(theta))^4-9.4531/((1.-0.39388e-1*h3(theta))*ln(10.-.39388*h3(theta))^2)-4.6603/((1.-0.38836e-1*h3(theta))*ln(10.-.38836*h3(theta))^2)-9.0393/((1.-0.37664e-1*h3(theta))*ln(10.-.37664*h3(theta))^2)-4.2631/((1.-0.35526e-1*h3(theta))*ln(10.-.35526*h3(theta))^2)-7.6824/((1.-0.32010e-1*h3(theta))*ln(10.-.32010*h3(theta))^2)-.25088/(1.-0.37632e-1*h3(theta))^4-.12919/(1.-0.19378e-1*h3(theta))^4-.11842/(1.-0.35526e-1*h3(theta))^4-.12941/(1.-0.38822e-1*h3(theta))^4+0.20833e-2/(1.+0.12500e-2*h3(theta))^4-0.19206e-1/(1.-0.28810e-2*h3(theta))^4-4.6507/((1.-0.19378e-1*h3(theta))*ln(10.-.19378*h3(theta))^2)-.26255/(1.-0.39384e-1*h3(theta))^4-.13182/(1.-0.39545e-1*h3(theta))^4-.25109/(1.-0.37664e-1*h3(theta))^4-3.2120/((1.-0.26767e-1*h3(theta))*ln(10.-.26767*h3(theta))^2) = 0]

ode2 := diff(SYS[2], theta); SYS2 := {ode2, SYS[1], SYS[3]}; bcs2 := {h1(0) = 0, h1(1) = 0, h2(0) = 0, h2(1) = 0, h3(0) = 0, h3(1) = 0, ((D@@1)(h1))(0) = 0, ((D@@1)(h1))(1) = 0, ((D@@1)(h3))(0) = 0, ((D@@1)(h3))(1) = 0}; bcs22 := eval[recurse](convert(SYS[2], D), `union`({theta = 1}, bcs2)); res2 := dsolve(`union`(`union`(SYS2, bcs2), {bcs22}), 'maxmesh' = 2024, numeric, method = bvp[middefer], range = 0 .. 1, abserr = 0.1e-3, output = listprocedure)

NULL



Download dsolve.mw

 


Hello Dr/Prof?sir?madam

i have problem on running the ode bcs

there is cos n sine in ther ode

any idea to solve this ?

i have attched it

thnks
Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Sc.mw .

Download Sc.mw

How can i over come convergence error, i am unable to apply approxsoln appropriately and continouation as well. regards

N := 5;

-(1/2)*Pr*n*x*(diff(f(x), x))*(diff(theta(x), x))-(1/2)*Pr*(n+1)*f(x)*(diff(theta(x), x))-(1/2)*(n+1)*(diff(diff(theta(x), x), x))+Pr*gamma*((1/4)*(n^2-3*n+3)*x^2*(diff(f(x), x))*(diff(diff(f(x), x), x))*(diff(theta(x), x))+(1/4)*(2*n^2+5*n+3)*f(x)*(diff(f(x), x))*(diff(theta(x), x))+(1/4)*n(n+1)*x*f(x)*(diff(diff(f(x), x), x))*(diff(theta(x), x))+(1/4)*(2*n^2+3*n-3)*x*(diff(f(x), x))^2*(diff(theta(x), x))+(1/4)*(n-1)*x^2*(diff(diff(f(x), x), x))*(diff(theta(x), x))+(1/2)*n*(n+1)*x*f(x)*(diff(f(x), x))*(diff(diff(theta(x), x), x))+(1/4)*(n^2-1)*(diff(f(x), x))^2*(diff(theta(x), x))+(1/4)*(n+1)^2*f(x)^2*(diff(diff(theta(x), x), x))+(1/4)*(n-1)^2*x^2*(diff(f(x), x))^2*(diff(diff(theta(x), x), x))) = 0

(1)

bc := (D(theta))(0) = -Bi*(1-theta(0)), theta(N) = 0, f(0) = 0, (D(f))(0) = 0, (D(f))(N) = 1;

(D(theta))(0) = -Bi*(1-theta(0)), theta(5) = 0, f(0) = 0, (D(f))(0) = 0, (D(f))(5) = 1

(2)

a1 := dsolve(subs(beta = .1, n = .5, Pr = 10, gamma = .1, Bi = 50, {bc, eq1, eq2}), numeric, method = bvp[midrich], abserr = 10^(-8), output = array([seq(.1*i, i = 0 .. 10*N)]))

Error, (in dsolve/numeric/BVPSolve) initial Newton iteration is not converging

 

``

 

Download ehtasham.mwehtasham.mw

Hi,
I want to plot stream lines from a stream function given by " psi = x*f(eta)+int(h(s), s = 0 .. eta) " where "f(eta)" and "h(eta)" are the solution of the differential equation given below:

restart;
with(linalg);
Digits := 24;

eq1:=diff(f(eta),eta,eta,eta)+f(eta)*diff(f(eta),eta,eta)-(diff(f(eta),eta))^2+1;
eq2 := diff(h(eta),eta,eta)+f(eta)*diff(h(eta),eta)-diff(f(eta),eta)*h(eta);
bc:=f(0)=0,D(f)(0)=0,D(f)(6)=1,h(0)=0,D(h)(6)=1;
A1:=dsolve({eq1,eq2,bc},numeric,method=bvp[midrich],abserr = 1.*10^(-10),output=operator):

How can I do this?

I want to solve system of non linear odes numerically.

I encounter following error

Error, (in dsolve/numeric/bvp) cannot determine a suitable initial profile, please specify an approximate initial solution

how to correct it

regards

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