Re: NIntegrate Problem
- To: mathgroup at smc.vnet.net
- Subject: [mg94631] Re: [mg94619] NIntegrate Problem
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Thu, 18 Dec 2008 07:21:17 -0500 (EST)
- References: <200812171156.GAA09649@smc.vnet.net>
- Reply-to: drmajorbob at longhorns.com
Possibly this is what you wanted:
Clear[w, g2]
w[t_?NumericQ, v_?NumericQ] :=
w[t, v] = (Abs@f[u])^2 /.
NDSolve[{f'[u] ==
E^(-((u^2 + u v)/8)) Sinc[(u + v)/2] E^(-I (t + 1/2) u),
f[-5] == 0}, f[u], {u, -5, 5}][[1]] /. {u -> 5}
g2[t_?NumericQ] := NIntegrate[E^(-(v^2/8)) w[t, v], {v, -7., 7.}]
g2[0]
56.8889
Bobby
On Wed, 17 Dec 2008 05:56:21 -0600, Kevin J. McCann
<Kevin.McCann at umbc.edu> wrote:
> I have the following double integral
>
> W[t_, v_] :=
> Abs[NIntegrate[
> E^(-((u^2 + u v)/8.))
> Sinc[(u + v)/2.] E^(-I (t + 0.5) u) , {u, -5., 5.}]]^2
> G2[t_] := NIntegrate[E^(-(v^2/8)) W[t, v], {v, -7., 7.}]
>
> G2[0.0]
>
> The last part produces this rather strange output, considering that the
> Abs[]^2 should not give out complex numbers.
>
> NIntegrate::inumr: The integrand E^(-0.5 I u-0.125 (<<1>>+<<1>>))
> Sinc[0.5 (u+v)] has evaluated to non-numerical values for all sampling
> points in the region with boundaries {{-5.,5.}}.
>
> NIntegrate::inumr: The integrand E^(-0.5 I u-0.125 (<<1>>-<<1>>))
> Sinc[0.5 (u-v)] has evaluated to non-numerical values for all sampling
> points in the region with boundaries {{-5.,5.}}.
>
> General::stop: "\!\(\*
> StyleBox[\"\\\"Further output of \\\"\", \"MT\"]\)\!\(\* StyleBox[
> RowBox[{\"NIntegrate\", \"::\", \"\\\"inumr\\\"\"}], \"MT\"]\)\!\(\*
> StyleBox[\"\\\" will be suppressed during this calculation.\\\"\",
> \"MT\"]\) "
>
> 56.8889
>
> One other interesting thing is that after all the complaining, it does
> produce an answer. Evaluate of the function W[t,v] above only produces
> real numbers. In addition, the integration is very slow. I got around
> the problem by building a Table of W, using Interpolation, and then
> integrating that - very fast, and no problems.
>
> Any ideas why I would get the above complaints?
>
> Thanks,
>
> Kevin
>
--
DrMajorBob at longhorns.com
- References:
- NIntegrate Problem
- From: "Kevin J. McCann" <Kevin.McCann@umbc.edu>
- NIntegrate Problem