Re: NIntegrate in NDSolve?

*To*: mathgroup at smc.vnet.net*Subject*: [mg89065] Re: NIntegrate in NDSolve?*From*: Szabolcs <szhorvat at gmail.com>*Date*: Sun, 25 May 2008 03:19:26 -0400 (EDT)*References*: <g18hon$kg7$1@smc.vnet.net>

On May 24, 9:57 am, EcoTheory <carroll.... at gmail.com> wrote: > Hello, This is my first Mathematica question ... of many to come, I'm sure= . My question is, can you use NIntegrate within NDSolve? My attempts lead to= this error: > > NIntegrate::inum : Integrand is non - numerical etc. > > Here is a simple example: > NDSolve[{y'[t] == NIntegrate[z y[t], {z, 0, 1}], y[0] == 1}, y[t],= {t, 0, 1}] > > As far as I can tell, Mathematica does not believe that y[t] is a number. = But shouldn't the numerical solver give y[t] as a number to NIntegrate? Yes, it does, but even before it gets a chance to substitute a number for y[t], the NIntegrate[ ... ] expression gets evaluated. We must prevent this somehow. Here is a possibility: fun[y_?NumericQ] := NIntegrate[z y, {z, 0, 1}] (This function only gets evaluated for numeric arguments) NDSolve[{y'[t] == fun[y[t]], y[0] == 1}, y, {t, 0, 1}] > > Obviously, Mathematica can do this problem easily enough using Integrate i= nstead of NIntegrate, but it cannot integrate the messier double integral in= the actual system of ODE's I want to solve. Thanks for suggestions.