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MathGroup Archive 2004

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Re: system of nonlinear differential equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48648] Re: system of nonlinear differential equations
  • From: V.Cejka at seznam.cz (Vasek)
  • Date: Wed, 9 Jun 2004 04:17:13 -0400 (EDT)
  • References: <90v42m$6se@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Boundary nonlinear problems can be solved by combination of FindRoot
and NDSolve commands. NDSolve must have exact numerical initial
conditions, but these conditions can be parameters substituted by
FindRoot iteration. Condition of FindRoot command is another boundary
condition evaluated from the result of NDSolve function. Actually,
syntax in mathematica is not easy and is different in version 4.x and
5.0. See:
http://library.wolfram.com/infocenter/MathSource/652/

In Mathematica 5.0 replace

y[n_][m_][IBguess_] := First[(y[n][r] /. Evaluate[sol[IBguess]]) /. 
 r->m]

 FindRoot[ (bign/2*y[1][1][IBguess] + y[2][1][IBguess] - bign/2 == 0),

 {IBguess, {1.5,1.3}}]

 with

 y[n_][m_][IBguess_?NumericQ] := First[(y[n][r] /. 
 Evaluate[sol[IBguess]])
/. r->m]

 FindRoot[ (bign/2*y[1][1][IBguess] + y[2][1][IBguess] - bign/2 == 0),
                  {IBguess, 1.5,1.3}]

On 10 Dec 2000 00:24:38 -0500, Bogdan Wasiluk wrote:
>
>How could I find solution of the system of nonlinear differential
equations?
>I can not solve them using DSolve or NDSolve, please see attached
file.
>I know that boundary conditions for DSolve should be at the same
point.
>
>Best regards,
>
>Bogdan 
>
>E-mail: bwasiluk at force.energy.kyoto-u.ac.jp


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