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Re: NIntegrate in NDSolve?

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  • Subject: [mg89065] Re: NIntegrate in NDSolve?
  • From: Szabolcs <szhorvat at>
  • Date: Sun, 25 May 2008 03:19:26 -0400 (EDT)
  • References: <g18hon$kg7$>

On May 24, 9:57 am, EcoTheory <carroll.... at> 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.

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