a problem with NIntegrate
- To: mathgroup at smc.vnet.net
- Subject: [mg119280] a problem with NIntegrate
- From: Ottofritz <ostpreussen at qq.com>
- Date: Sat, 28 May 2011 07:20:44 -0400 (EDT)
Hello, I encounter a strange problem with NIntegrate:
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g1[a_, r1_, r2_] := -r1 BesselI[1, r1 a] StruveL[0, r1 a] +
r2 BesselI[1, r2 a] StruveL[0, r2 a] +
r1 BesselI[0, r1 a] StruveL[1, r1 a] -
r2 BesselI[0, r2 a] StruveL[1, r2 a];
u[w_, \[Gamma]_, \[Theta]_] :=
w (Sin[\[Gamma]] Sin[\[Theta]] - I Cos[\[Gamma]]);
v[w_, \[Gamma]_, \[Theta]_] :=
w (Sin[\[Gamma]] - I Cos[\[Gamma]] Sin[\[Theta]]);
\[Lambda][w_, \[Omega]_, \[Mu]r_, \[Kappa]_] := (
Sqrt[w^2 +
4 \[Pi] I (10^-7) \[Omega] \[Mu]r \[Kappa] ] - \[Mu]r w)/(
w (Sqrt[w^2 +
4 \[Pi] I (10^-7) \[Omega] \[Mu]r \[Kappa] ] + \[Mu]r w));
wx[\[Omega]_, \[Mu]r_, \[Kappa]_, \[Gamma]_, H_, h_, r1_, r2_] :=
NIntegrate[(\[Lambda][
w, \[Omega], \[Mu]r, \[Kappa]] w (Cos[\[Theta]])^2)/(u[
w, \[Gamma], \[Theta]])^3 Exp[-2 w (H + h Cos[\[Gamma]])] (Exp[
2 h w Cos[\[Gamma]]] - 1)^2 (g1[u[w, \[Gamma], \[Theta]], r1,
r2])^2, {w, 0, \[Infinity]}, {\[Theta], -\[Pi]/2, \[Pi]/2}];
=====================================
To be evaluated is following expression:
wx[100 \[Pi], 100, 10^7, \[Gamma], 0.1, 0.03, 0.03, 0.08]
when the value of \[Gamma] is between 0 to \[Pi]/4, wx[] can be carried out easily; but if the value of \[Gamma] is between \[Pi]/4 to \[Pi]/2, wx[] can't be carried out and the program gives following message:
=================================
NIntegrate::inumri: "The integrand (E^(-0.248541 w)\(-1+E^(0.048541 w))^2\(-100\w+Sqrt[40000 I \[Pi]^2+w^2])\Cos[\[Theta]]^2\(<<1>>)^2)/(w^3\(100\w+Sqrt[40000 I \[Pi]^2+w^2])\(-(1/4) I (1+Sqrt[5])+Sqrt[5/8-1/8 Power[<<2>>]] Sin[\[Theta]])^3) has evaluated to Overflow, Indeterminate, or Infinity for all sampling points in the region with boundaries {{0.,1.70984*10^14},{-1.57078741253953310081093168882465649360824500035960227251052856445,-1.37444678594553448824910901748808100819587707519531250000000000000}}."
Could anyone give me some advices?Thanks a lot!