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MathGroup Archive 1996

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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

**************************************************************************
* Paul A. Rubin                                  Phone: (517) 432-3509   *
* Department of Management                       Fax:   (517) 432-1111   *
* Eli Broad Graduate School of Management        Net:   RUBIN at MSU.EDU    *
* Michigan State University                                              *
* East Lansing, MI  48824-1122  (USA)                                    *
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Mathematicians are like Frenchmen:  whenever you say something to them,
they translate it into their own language, and at once it is something
entirely different.                                    J. W. v. GOETHE

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