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Re: differential equation
Posted:
Sep 20, 1996 12:51 AM


In article <51c4mm$9no@ralph.vnet.net>, Ralph Gensheimer <ralphg@spock.physik.unikonstanz.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) 4323509 * * Department of Management Fax: (517) 4321111 * * Eli Broad Graduate School of Management Net: RUBIN@MSU.EDU * * Michigan State University * * East Lansing, MI 488241122 (USA) * ************************************************************************** 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



