Re: Numerical integration inside numerical integration
- To: mathgroup at smc.vnet.net
- Subject: [mg48823] Re: Numerical integration inside numerical integration
- From: nafod40 <noneya at business.com>
- Date: Fri, 18 Jun 2004 02:12:45 -0400 (EDT)
- Organization: Penn State University, Center for Academic Computing
- References: <cark1d$r7v$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
blah12 at mail.com wrote:
> Hello all,
>
> I'm trying to solve numerically an integral like,
>
>
> A=some_value
> NIntegrate[f[y,u]*Log[1+NIntegrate[g[y,u,s], {s, A, \[Infinity]}]],
> {u, -\[Infinity],\[Infinity]},{y, -\[Infinity],\[Infinity]}]
>
> I know I am doing this wrong as the inner integration fails because
> it doesn't have specific numerical values for y and u.
> I guess Mathematica doesn't perform numerical integrations from the
> outside to the inside (and so passing each time values of y,u to
> the inner integration).
>
> How can this problem be solved with Mathematica please ?
If you use patterns to force the inner integration to only work when it
is passed numerical values, things should work OK.
You see similar effects when you have functions inside of things like
FindRoot, where Mathematica attempts to immediately resolve the inner term, and
you don't want it to.