Re: NIntegrate in NDSolve?

• To: mathgroup at smc.vnet.net
• Subject: [mg7] Re: [mg89038] NIntegrate in NDSolve?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 25 May 2008 02:06:25 -0400 (EDT)

```Use symbolic solution

sol1 = y[t] /.
DSolve[{y'[t] == Integrate[z y[t], {z, 0, 1}], y[0] == 1}, y[t], t][[1]]

E^(t/2)

Plot[sol1, {t, 0, 1}]

Or use symbolic solution for intermediate step

sol2 = y[t] /.
NDSolve[{y'[t] == Integrate[z y[t], {z, 0, 1}], y[0] == 1},
y[t], {t, 0, 1}];

Plot[sol2, {t, 0, 1}]

Or restrict the numerical integration to evaluate only with numerical arguments.

f[a_, t_?NumericQ] := NIntegrate[z a, {z, 0, 1}];

sol3 = y[t] /. NDSolve[{y'[t] == f[ y[t], t], y[0] == 1}, y[t], {t, 0, 1}];

Plot[sol3, {t, 0, 1}]

Bob Hanlon

---- EcoTheory <carroll.ian 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?
>
> Obviously, Mathematica can do this problem easily enough using Integrate instead 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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