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how to solve nonlinear ode higher ode system with bc?d

Posted 6 years ago
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I had attach a file. I want to improve it? How can this be done? I don't want to solve it numerically with shooting. Are there any methods?

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You are far more likely to get help if you put your Mathematica code and comments into your post directly and not in an external pdf file. It is suggested you do that immediately.

i have attach a problem can someone solve this and attched back? there is error

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Posted 6 years ago

There are many misunderstandings in your code.

NDSolve requires equations, f'[x]==0 and not just f'[x].

NDSolve requires that all variables, other than the functions being solved for, have been assigned constant numeric values before the NDSolve,

FindRoot when looking for a solution in more than one variable requires that those variables be inside another layer of { }, thus FindRoot[equation,{{x,0,1},{y,1,5}}] and not FindRoot[equation,{x,0,1},{y,1,5}]

It appears that I do not have the appropriate unicode font installed for your notebook. I have changed those unicode characters into other names and may have made some errors in doing this.

I have made many changes to your code in trying to get it to function. You should carefully check to see that I have not introduced errors.

b=3; a=0.; NB=0.1; NT=0.1; LE=10; Pr=6.8; Nr=0.5; gamma=0.2; Lb=1; Pe=1; Rb=2; lamda=0.1; A= -NT/NB;
fpp = 0.5; tpp = 0.42; gpp = -0.40; hpp = -0.1; upp = 0.1;
{f28A, f28a, f28a0, f28a1} = RandomReal[{-1, 1}, 4];
{finit1, finit2, finit3, finit4, finit5} = {f[b], t[b], g[b], h[b], u[b]} /. 
  NDSolve[{Pr f'''[x] + 0.6 f[x] f''[x] - 0.2 f'[x]^2 + 0.4 x h'[x] - 0.4 h[x] f28a0 == 0, 
     t''[x] + 0.6 f[x] t'[x] + NB t'[x] g'[x] + NT t'[x]^2 == 0, 
     g''[x] + t''[x] (NT/NB) + 0.6 LE f[x] g'[x] f28a0 == 0, 
     h'[x] - Pr t[x] + Nr Pr g[x] + Rb u[x] f28a0 == 0, 
     u''[x] - Pe (g'[x] u'[x] + u[x] g''[x]) + 0.6 Lb f[x] u'[x] f28a0 == 0,
     f[0] f28a0 == 0, 
     f''[0] f28a fpp == 0,
     f'[0] f28a lamda + a fpp == 0, 
     t'[0] f28a tpp == 0,
     t[0] f28a - 1 - (tpp)/(gamma) == 0, 
     g'[0] f28aA tpp == 0,
     g[0] f28a gpp == 0,
     h[0] == hpp, 
     u[0] f28a1 == 0,
     u'[0] == upp}, {f, t, g, h, u}, {x, 0, b}][[1]]

which returns a value

{7.21666, -3.26415, 0., -65.997, 0.463137}

I have not yet incorporated your FindRoot into this code because I simply cannot understand that part of your code.

Please check this against your original notebook, character by character, to see if I have made any errors. If you can fix any of my errors, incorporate this into your original notebook, describe clearly any remaining errors and what you are trying to accomplish then perhaps someone can see a way to finish the corrections.

tq bill SImpson.. you are PHD student? DR? Professor?

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