Items tagged with bvp

i tried to solve a nonlinear ode with numerical method but maple can't solve it and this error occur:

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

my maple codes are attached below:

numeriacal_sol.mw

can any help me?


Please help me on this :

restart; with(PDETools), with(plots)

n := .3:

Eq1 := (1-n)*(diff(f(x, y), `$`(y, 3)))+(1+x*cot(x))*f(x, y)*(diff(f(x, y), `$`(y, 2)))-(diff(f(x, y), y))/Da+(diff(f(x, y), y))^2+n*We*(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), `$`(y, 3)))+sin(x)*(theta(x, y)+phi(x, y))/x = x*((diff(f(x, y), y))*(diff(f(x, y), y, x))+(diff(f(x, y), `$`(y, 2)))*(diff(f(x, y), x))):

Eq2 := (diff(theta(x, y), `$`(y, 2)))/Pr+Nt*(diff(theta(x, y), y))^2/Pr+Nb*(diff(phi(x, y), y))*(diff(theta(x, y), y))/Pr+(1+x*cot(x))*f(x, y)*(diff(theta(x, y), y)) = x*((diff(f(x, y), y))*(diff(theta(x, y), x))+(diff(theta(x, y), y))*(diff(f(x, y), x))):

Eq3 := Nb*(diff(phi(x, y), `$`(y, 2)))/(tau*Pr)+Nt*(diff(theta(x, y), `$`(y, 2)))/(tau*Pr)+(1+x*cot(x))*f(x, y)*(diff(phi(x, y), y)) = x*((diff(f(x, y), y))*(diff(phi(x, y), x))+(diff(phi(x, y), y))*(diff(f(x, y), x))):

ValWe := [0, 5, 10]:

bcs := {Nb*(D[2](phi))(x, 0)+Nt*(D[2](theta))(x, 0) = 0, f(0, y) = ((1/12)*y)^2*(6-8*((1/12)*y)+3*((1/12)*y)^2), f(x, 0) = 0, phi(0, y) = -.5*y, phi(x, 12) = 0, theta(0, y) = (1-(1/12)*y)^2, theta(x, 0) = 1, theta(x, 12) = 0, (D[2](f))(x, 0) = Da^(1/2)*(D[2, 2](f))(x, 0)+Da*(D[2, 2, 2](f))(x, 0), (D[2](f))(x, 12) = 0}:

pdsys := {Eq1, Eq2, Eq3}:

p1 := ans[1]:-plot(theta(x, y), x = 1, color = blue):

plots[display]({p1, p2, p3})

 

``


 

Download untitle_2_(1).mw

Respected member!
Please help me to find the solution of attached problem.

 


> subject to boundary conditions


``

 

 

NULL

restart

alpha := evalf(2*Pi*(1/180)); EP := .2; lambda := .1; HA := 5; RE := 20

ODEforNum := (1+EP)*(((D@@3)(F))(r)+4*alpha^2*(D(F))(r))+2*alpha*RE*F(r)*(D(F))(r)-HA*alpha^2*(D(F))(r)-3*EP*lambda*((1/2)*(D(F))(r)^2*((D@@3)(F))(r)+(D(F))(r)*((D@@2)(F))(r)^2)/alpha^2-EP*lambda*(72*F(r)^2*(D(F))(r)+2*(D(F))(r)^3+32*F(r)*(D(F))(r)*((D@@2)(F))(r)+2*F(r)^2*((D@@3)(F))(r)) = 0

1.2*((D@@3)(F))(r)-0.243693936e-3*(D(F))(r)+1.396263402*F(r)*(D(F))(r)-24.62104762*(D(F))(r)^2*((D@@3)(F))(r)-49.24209525*(D(F))(r)*((D@@2)(F))(r)^2-1.44*F(r)^2*(D(F))(r)-0.4e-1*(D(F))(r)^3-.64*F(r)*(D(F))(r)*((D@@2)(F))(r)-0.4e-1*F(r)^2*((D@@3)(F))(r) = 0

 
 

 

BCSforNum := F(0) = 1, (D(F))(0) = 0, F(1) = 0

Digits := 15

15

(2)

numsol := dsolve({BCSforNum, ODEforNum}, numeric, output = listprocedure)

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

 
 

 

 

 

 

 

 

 

Download MapleN.mw

Respected member!
Please help me to find the solution of attached problem,  I am a new user so please forgive any mistakes.maple.mwmaple.mw

Hello, Sir 

I tried to execute the program for a set values for more than one parameter but it is not existing, please can you do a favor for me in this case, that is how to write a program to execute set of values for more than one parameter at a time and how to plot the graph?

 

stretching_cylinder_new.mw

 

hi.

how i can dsolve this differential equations?

thanks

ich.mw
 

restart; Digits := 50; dsol1 := dsolve({diff(F(eta), eta, eta, eta)+.5*H(eta)*((diff(F(eta), eta))^2+F(eta)*(diff(F(eta), eta, eta)))/G(eta)^2+2*(diff(G(eta), eta))*(diff(F(eta), eta, eta))/G(eta)-(diff(H(eta), eta))*(diff(F(eta), eta, eta))/H(eta) = 0, diff(G(eta), eta, eta)+H(eta)*((diff(F(eta), eta))*G(eta)+.5*F(eta)*(diff(eta, eta)))/G(eta)^2+2*(diff(G(eta), eta))^2/G(eta)-((diff(H(eta), eta))*(diff(H(eta), eta)))/H(eta)+(diff(F(eta), eta, eta))^2-(H(eta)/G(eta))^2 = 0, diff(H(eta), eta, eta)+(.5*1.3)*H(eta)*(5*(diff(F(eta), eta))*H(eta)+F(eta)*(diff(H(eta), eta)))/G(eta)^2+2*(diff(G(eta), eta))*(diff(H(eta), eta))/G(eta)-(diff(H(eta), eta))^2/H(eta)+(1.3*1.44)*H(eta)*(diff(F(eta), eta, eta))/G(eta)-(1.3*1.92)*(H(eta)/G(eta))^3 = 0, F(0) = 0, G(0) = 0, H(0) = 0, (D(F))(0) = 1, (D(F))(1) = 0, (D(G))(0) = 0, (D(H))(0) = 0}, 'maxmesh' = 900, numeric, output = listprocedure, method = bvp[middefer], abserr = 0.1e-2); fy := eval(F(eta), dsol1)

Error, invalid input: eval received dsol1, which is not valid for its 2nd argument, eqns

 

 

NULL


 

Download ich.mw

 

Respected member!
Please help me to find the solution of attached problem, I am a new user so pleaes forgive any mistakes.
 

``


``


``

NULL

NULL

restart

R := 2.0

2.0

(1)

ODEforNum := r^3*((D@@4)(F))(r)+r^2*R*((D@@3)(F))(r)*(F(r)-2/R)+R*((D(F))(r)-r*((D@@2)(F))(r))*(r*(D(F))(r)+3*(F(r)-1/R)) = 0:

numsol := dsolve({BCSforNum, ODEforNum}, numeric, output = listprocedure)

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

 

``


 

Download mplprimes.mw


 

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.

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

a := 1.9501*10^24;

b := .3306;

c := 2.99792458*10^10;

d := 2.035;

pi := 3.143;

eps := 3.8220*10^35;

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

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

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

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

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

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

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

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

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

and for the progam please check the following link

stretching_cylinder_new1.mw

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

Thanks 
 

NULL

restart

Digits := 10

with(ODETools)

with(student)

with(plots)

inf := 4.2

NULL

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

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

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

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

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

(1)

S1(0)

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

(2)

S1(inf)

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

(3)

NULL

a := 1.88379445589794-.510658709628757*inf

-.260972124

(4)

inf := 10

NULL

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

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

(5)

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

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

(6)

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

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

(7)

S11(0)

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

(8)

S11(inf)

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

(9)

NULL

NULL

inf := 4.2

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

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

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

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

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

(10)

S2(0)

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

(11)

S2(inf)

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

(12)

"b:="

inf := 10

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

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

(13)

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

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

(14)

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

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

 

NULL

NULL


 

Download kuikennnnnn.mw
 

NULL

restart

Digits := 10

with(ODETools)

with(student)

with(plots)

inf := 4.2

NULL

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

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

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

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

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

(1)

S1(0)

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

(2)

S1(inf)

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

(3)

NULL

a := 1.88379445589794-.510658709628757*inf

-.260972124

(4)

inf := 10

NULL

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

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

(5)

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

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

(6)

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

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

(7)

S11(0)

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

(8)

S11(inf)

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

(9)

NULL

NULL

inf := 4.2

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

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

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

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

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

(10)

S2(0)

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

(11)

S2(inf)

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

(12)

"b:="

inf := 10

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

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

(13)

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

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

(14)

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

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

 

 

 

 

Help me, please!

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

 

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

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

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

Hi

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

error:

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

Turbulent2-kw.mw

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

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

 

NULL

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

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

 

``



Download Turbulent2-kw.mw

 

 

 

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