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Re: NIntegrate Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg94626] Re: NIntegrate Problem
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 18 Dec 2008 07:20:23 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <giapeb$9e9$1@smc.vnet.net>

Kevin J. McCann 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?

Hi Kevin,

The function *W* should be defined in such a way that it is evaluated 
only when all its arguments are numeric so it returns a numeric value 
too. For instance,

In[1]:= Clear[W, G2]
W[t_?NumericQ, v_?NumericQ] :=
  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]

Out[4]= 56.8889

Best regards,
-- Jean-Marc


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