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NIntegrate Problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg94619] NIntegrate Problem
  • From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
  • Date: Wed, 17 Dec 2008 06:56:21 -0500 (EST)
  • Organization: University System of Maryland

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


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