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MathGroup Archive 2007

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Integration of Singular function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79923] Integration of Singular function
  • From: Khandelwal <ratneshk at gmail.com>
  • Date: Thu, 9 Aug 2007 05:11:38 -0400 (EDT)

Hello,

I am having trouble integrating the following functions in
Mathematica

II=Table[{t,
  NIntegrate[
    rf1[x, y], {y, -\[Infinity], 0}, {x, -\[Infinity], \[Infinity]},
    MaxRecursion -> 60, Method -> MonteCarlo[24],
    MaxPoints -> 500000000] +
   NIntegrate[
    rf2[x, y], {y, 0, \[Infinity]}, {x, -\[Infinity], \[Infinity]},
    MaxRecursion -> 60, Method -> MonteCarlo[24],
    MaxPoints -> 500000000]}, {t, 0.0001, 5, 0.2}]


rf1[x_,y_]=(0.0666667 \[ExponentialE]^-((-1 + x)^2 + (-1 + y)^2)/(4 t)
   Im[((1 + 0.1516 \[ImaginaryI]) (1 + x + \[ImaginaryI] y) ((
    1 + x + \[ImaginaryI] y)/(-1 + x + \[ImaginaryI] y))^(
   0.0758 \[ImaginaryI]))/(-1 + (x + \[ImaginaryI] y)^2)^(3/2)])/t

rf1[x_,y_]=(0.621099 (\[ExponentialE]^-((-1 + x)^2 + (-1 + y)^2)/(4 t) -
   1/3 \[ExponentialE]^-((-1 + x)^2 + (1 + y)^2)/(4 t)) Im[((1 +
     0.1516 \[ImaginaryI]) (1 + x + \[ImaginaryI] y) ((
    1 + x + \[ImaginaryI] y)/(-1 + x + \[ImaginaryI] y))^(
   0.0758 \[ImaginaryI]))/(-1 + (x + \[ImaginaryI] y)^2)^(3/2)])/t

My problem is though i'm taking too large value of MaxPoints
(MaxPoints -> 500000000), because of that it's takes lot of time, but
still for some inital small value of t(0.0001) its not conversing. I
want to plot (t,II), where t->(0,5). Just wondering if there is other
better way of dealing this integration!!

-- 
Regards,
Ratnesh Khandelwal
IISc,Bangalore,INDIA


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