Items tagged with numeric


 

refresh

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.

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]

 

 

 

 

Let us consider the improper integral

int((abs(sin(2*x))-abs(sin(x)))/x, x = 0 .. infinity);

Si(Pi)-Si((1/2)*Pi)+sum(-(-1)^_k*Si(Pi*_k)+signum(sin((1/2)*Pi*_k))*Si((1/2)*Pi*_k)+Si(Pi*_k+Pi)*(-1)^_k-signum(cos((1/2)*Pi*_k))*Si((1/2)*Pi*_k+(1/2)*Pi), _k = 1 .. infinity)
                    

Mathematica 11 produces a similar expression and a warning

Integrate::isub: Warning: infinite subdivision of the integration domain has been used in computation of the definite integral \!\(\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Infinity]\)]\(\*FractionBox[\(\(-Abs[Sin[x]]\) + Abs[Sin[2\ x]]\), \(x\)] \[DifferentialD]x\)\). If the integral is not absolutely convergent, the result may be incorrect.

Up to Pedro Tamaroff http://math.stackexchange.com/questions/61828/proof-of-frullanis-theorem , the answer is 2/Pi*ln(2) because of 

J := int(abs(sin(2*x))-abs(sin(x)), x = 0 .. T) assuming T>2;
-1/2-signum(sin(T))*signum(cos(T))*cos(T)^2+(1/2)*signum(sin(T))*signum(cos(T))+cos(T)*signum(sin(T))+floor(2*T/Pi)

B := limit(J/T, T = infinity);
                               2 /Pi

K := x*(int((abs(sin(2*t))-abs(sin(t)))/t^2, t = x .. 1)) assuming x>0,x<1;

     2*sin(x)*cos(x)-2*Ci(2*x)*x+Ci(x)*x+sin(1)*x-sin(2)*x+2*Ci(2)*x-Ci(1)*x-sin(x)

                         
A := limit(K, x = 0, right);
                               0

Its numeric calculation results 

evalf(Int((abs(sin(2*x))-abs(sin(x)))/x, x = 0 .. infinity));
                        Float(undefined)

which seems not to be true.

The question is: how to obtain the reliable results for it with Maple, both symbolic and numeric? 

I faced difficulity in solving this problem. Can you help 

Consider the expression
sum((-1)^n*exp(beta*n)/n^2, n = 1 .. infinity)
 Build a function to calculate an approximation for the value of the given expression for
any value for B
 

Dear all,

I need to transforme these equation from time domain to frequency domain with fourier transforms and solve it in frequency domain but i received the flowing error

any helps

thank you !

 

``

restart:with(inttrans):

E:=1;L:=1;

1

 

1

(1)

 

equ := arccos(y(t)/R)*R*L*(diff(y(t), `$`(t, 1)))*abs(diff(y(t), `$`(t, 1)))+diff(y(t), `$`(t, 2))+m*sin(omega*t+k*R*sin(`&theta;l`))+arccos(y(t)/R);

arccos(y(t)/R)*R*(diff(y(t), t))*abs(diff(y(t), t))+diff(diff(y(t), t), t)+m*sin(omega*t+k*R*sin(`&theta;l`))+arccos(y(t)/R)

(2)

eq:=fourier(equ,t,omega);

((1/2)*I)*m*fourier(exp(-I*omega*t), t, omega)*exp(-(1/2)*k*R*exp(I*`&theta;l`)+(1/2)*k*R*exp(-I*`&theta;l`))-omega^2*fourier(y(t), t, omega)-((1/2)*I)*m*fourier(exp(I*omega*t), t, omega)*exp((1/2)*k*R*exp(I*`&theta;l`)-(1/2)*k*R*exp(-I*`&theta;l`))+R*fourier(arccos(y(t)/R)*(diff(y(t), t))*abs(diff(y(t), t)), t, omega)+fourier(arccos(y(t)/R), t, omega)

(3)

csi := y(0) = 0.2e-1, (D(y))(0) = 0;

y(0) = 0.2e-1, (D(y))(0) = 0

(4)

sol := dsolve({csi, eq}, numeric, maxfun = 1000000000)

Warning, The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)

 

Error, (in solve) cannot solve expressions with fourier(arccos(Y[1]/R)*YP[1]*abs(YP[1]), t, omega) for YP[1]

 

Code :

Download Fourier_TRAns_MAPLEprime.mwFourier_TRAns_MAPLEprime.mw

Dears;

Hope everyone is fine. I am try to find the numerical solutions of system of nonlinear algabric equation via newton's raphson method in the attached file but failed. Please see the attachment and try to correct. You can solve it least square method if possible. I am waiting your positive response. 

Help_in_Newton.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Email: muhammadusman@pku.edu.cn

For my fdiff graph, it seems that the cirtical points appear to be jaggered or not smooth. Anyone nows what seem to be the problem? i tried increasing the numpoints but it did not work:( I am open to all opinions. Thanks:)

 

fyp2.mw

For the ODE system with boundary conditions, I was able to obtain solutions for n=0, but not for n>0. I obtained the error, Initial newton iteration is not converging. Anyone knows the solution for this? I am open to all suggestions and any help would be greatly appreciated:)

 

ODE_solution.mw

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, I have been trying to solve the Schrodinger equation for harmonic oscillators using dsolve and plot the the wavefunctions for the different energy levels. However I am struggling to plot all the different wavefuntions on the same plot. I also want to normalize the wavefunctions to help compare their shapes and values. Here's my code:- schro := {diff(psi(x), x, x)-(alpha*x^4+x^2-energy)*psi(x) = 0}; // d / d \\ / 4 2 \ \ { |--- |--- psi(x)|| - \alpha x + x - energy/ psi(x) = 0 } \\ dx \ dx // / ic := {psi(3) = 0, (D(psi))(3) = 1}; {psi(3) = 0, D(psi)(3) = 1} schro1 := subs(energy = 3.30687, alpha = .1, schro); soln1 := dsolve(schro1 union ic, {psi(x)}, type = numeric); // d / d \\ / 4 2 \ \ { |--- |--- psi(x)|| - \0.1 x + x - 3.30687/ psi(x) = 0 } \\ dx \ dx // / proc(x_rkf45) ... end; with(plots); [animate, animate3d, animatecurve, arrow, changecoords, complexplot, complexplot3d, conformal, conformal3d, contourplot, contourplot3d, coordplot, coordplot3d, densityplot, display, dualaxisplot, fieldplot, fieldplot3d, gradplot, gradplot3d, implicitplot, implicitplot3d, inequal, interactive, interactiveparams, intersectplot, listcontplot, listcontplot3d, listdensityplot, listplot, listplot3d, loglogplot, logplot, matrixplot, multiple, odeplot, pareto, plotcompare, pointplot, pointplot3d, polarplot, polygonplot, polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions3d, shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot3d, tubeplot] odeplot(soln1, [x, psi(x)], -3 .. 3); Thank in advance

hi..i have a problem for solving this nonlinear differential equationerror.mw

restart; Digite := 200; L := 100*10^(-9)

1/10000000

(1)

EQ11 := -3.000000000*10^(-8)+3.815358072*sin(3.141592654*10^7*x)+9.534375000*10^(-30)*(diff(w(x), x, x, x, x))-2.383593750*10^(-60)*(diff(w(x), x, x, x, x, x, x))-5.085000000*10^(-13)*(diff(w(x), x))*(diff(u(x), x, x))-7.627500000*10^(-13)*(diff(w(x), x))^2*(diff(w(x), x, x))-5.085000000*10^(-13)*(diff(w(x), x, x))*(diff(u(x), x))+0.2410290000e-5*(diff(w(x), x, x)):

EQ2 := 5.650000000*10^(-20)*(diff(u(x), x, x, x, x))-226000000000*(diff(u(x), x, x))-226000000000*(diff(w(x), x))*(diff(w(x), x, x)):

dsys3 := {EQ11, EQ2, u(0) = 0, u(L) = 0, w(0) = 0, w(L) = 0, (D(u))(0) = 0, (D(u))(L) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(L) = 0, ((D@@4)(w))(0) = 0, ((D@@4)(w))(L) = 0}; res := dsolve(dsys3, numeric, initmesh = 1024, abserr = 0.1e-4); res(0.1e-9)

res(0.1e-9)

(2)

############################################################CHANGE OF VARIABLE:::           x=y*L

bcs := {u(0) = 0, u(L) = 0, w(0) = 0, w(L) = 0, (D(u))(0) = 0, (D(u))(L) = 0, ((D@@2)(w))(0) = 0, ((D@@2)(w))(L) = 0, ((D@@4)(w))(0) = 0, ((D@@4)(w))(L) = 0}; sys := {EQ11, EQ2}; sys2 := PDEtools:-dchange({x = L*y, u(x) = g2(y), w(x) = g1(y)}, sys, [g1, g2, y]); solve(sys2, {diff(g2(y), y, y, y, y), diff(g1(y), y, y, y, y, y, y)}); bcs3 := {g1(0) = 0, g1(1) = 0, g2(0) = 0, g2(1) = 0, (D(g2))(0) = 0, (D(g2))(1) = 0, ((D@@2)(g1))(0) = 0, ((D@@2)(g1))(1) = 0, ((D@@4)(g1))(0) = 0, ((D@@4)(g1))(1) = 0}; res3 := dsolve(`union`(sys2, bcs3), numeric, maxmesh = 2024, abserr = 0.1e-4); plots:-odeplot(res3, [seq([y, (cat(g, i))(y)], i = 1 .. 2)], 0 .. 1)

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

 

``

 

Download error.mw

please help me

thanks...

 

Hi guys,

 

I am trying to solve a Fredholm equation of the second kind using Maple. An analytical expression cannot be in principle found. I was wondering whether Maple does numerical evaluation of such integral equations. Please see the equation in attach. Any help is highly appreciated.

Thanks

F

 

Question.mw

Dear Community,

Would someone have a good and easy to understand/implement description of the Den Iseger algorithm for the numerical inversion of Laplace transform? Even better if someone would have a Maple script to do it, that would be superb.

Tx in advance,

best regards

Andras

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

 

 

 

I have recently acquired Maple 2016 and wanted to see how its numerical integration compared to previous version (in this instance, 2015 and 18). This integration is a tougher problem than the usual "textbook" case using a well behaved function. The integrand presented in the worksheet below is a small example but it can get much larger.

I am calculating a triple integral numerically from a function read in from a file which contains Laguerre polynomials. Some simplifications are done first and then that is fed into the integration. In the example script below the input has been put into the program to make it simpler.

So far it appears Maple 18 is faster than 2015 (in this case anyway) and 2016 does not appear to like the syntax I am using even though it runs fine on 18 and 2015 (it does not like the simplify(expr1,LaguerreL) or sqrt parts).

Looking at the stats of the calculation runs:

Maple 18:

memory used=0.52MiB, alloc change=0 bytes, cpu time=20.33s, real time=20.49s, gc time=0ns

answer = 0.160262735437965


Maple 2015:

memory used=350.84KiB, alloc change=0 bytes, cpu time=28.77s, real time=29.24s, gc time=0ns

answer = 0.160262735437309

What is interesting is that Maple 18 is allocating more memory in order to solve the problem compared to 2015. Does anyone have any ideas why this is occuring? Also has there been a syntax change from 2015 -> 2016 which I have not been aware of. Is there a different way to write the script to run in 2016?

Here is the worksheet:

Maple_numeric_speed.mw

Thank you in advance

- Yeti

1 2 3 4 5 6 7 Last Page 1 of 25