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) * ************************************************************************** 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 ==== [MESSAGE SEPARATOR] ====