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Topic: differential equation
Replies: 2   Last Post: Sep 20, 1996 12:51 AM

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Paul A. Rubin

Posts: 397
Registered: 12/7/04
Re: differential equation
Posted: Sep 20, 1996 12:51 AM
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In article <51c4mm$9no@ralph.vnet.net>,
Ralph Gensheimer <ralphg@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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