       Re: differential equation

• To: mathgroup at smc.vnet.net
• Subject: [mg4825] Re: differential equation
• From: rubin at msu.edu (Paul A. Rubin)
• Date: Fri, 20 Sep 1996 01:12:44 -0400
• Organization: Michigan State University
• Sender: owner-wri-mathgroup at wolfram.com

```In article <51c4mm\$9no at ralph.vnet.net>,
Ralph Gensheimer <ralphg at spock.physik.uni-konstanz.de> wrote:
->dear group,
->
->i have the folowing problem:
->
->in an ordinary differential equation system,
->(solution functions are  y1(r), y2(r), y3(r) ) is an integration in
another variable x.
->and in this integral there is also the solution function y3(r).
->r and x are independent.
->the problem has the following structure:
->
->NDSolve[{y1'[r] == y2[r],
->         y2'[r] == -(2/r)*y2[r]+
->
(-y1[r])^(3/2)*NIntegrate[x^(1/2)/(Exp[x+y3[r]]-1),{x,0,Infinity}],
->         y1[r]*y3'[r] == y2[r],
->                                 y1[0.001]==-1000,
->                                 y2[0.001]==0,
->                                 y3[0.001]==0 },{y1,y2,y3},{r,0.001,0.2}]
->
->can you give me ideas to solve this problem ?
->
->ralph

Maybe a successive approximation approach?  Replace the instance of y3[r]
in the integrand (only) with a new function y4[r].  Initially define
y4[r_]:=0.  Run NDSolve (still solving only for y1, y2 and y3).  Redefine
y4[r_]:= y3[r].  Iterate ad nauseum, and hope it converges?

Caveat:  I don't do differential equations, so I have no idea if this will
in fact converge.  It might just be a new way to waste cpu cycles.

-- Paul

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* Paul A. Rubin                                  Phone: (517) 432-3509   *
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