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Integral with singularities

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116666] Integral with singularities
  • From: "gmarkowsky at gmail.com" <gmarkowsky at gmail.com>
  • Date: Wed, 23 Feb 2011 05:24:46 -0500 (EST)

Hello all,

I am doing

NIntegrate[
 1/Sqrt[(x^2 + y^2) ((x - 1)^2 + 
      y^2) ((x - a)^2 + (y - b)^2)], {x, -3, 3}, {y, -3, 3}]

Somehow it is not working very well. This doesn't seem to be a particularly difficult request but Mathematica is having trouble. It keeps saying stuff like

NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>

NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after 18 recursive bisections in x near {x,y} = {1.,2.06474}. NIntegrate obtained 76.80413981137505` and 101.86483781265876` for the integral and error estimates. >>

I guess that near 0, 1, and a+bi the integrand blows up. I have tried to exclude small areas around those points, but I don't seem to be doing it right. Can anyone help?

Greg


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