A NIntegrate question

*To*: mathgroup at smc.vnet.net*Subject*: [mg52029] A NIntegrate question*From*: acsl at dee.ufrj.br (Antonio Carlos Siqueira)*Date*: Sun, 7 Nov 2004 01:04:44 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Dear All, I need to find the Inverse Fourier Transform of an expression involving Sqrt, Exp and Bessel Functions. As my interest is in the numerical response I am trying to use NIntegrate for frequency to time transform. In fact I am using it to have a Fourier Cossine transform. My problem is that I can only find an answer if I use interpolation for the frequency domain function. I was wondering if anybody can give me a help in trying to use NIntegrate to solve this problem. What I have tried didn´t work that well. Any comments are welcome. Regards Antonio Here comes my functions.... zint[s_, rhoc_:8.82573*10^-8, rc_:0.0203454, mu_:4.0 Pi 10^-7] := Sqrt[s mu/rhoc] rhoc/(2 Pi rc)BesselI[0, Sqrt[s mu/rhoc] rc]/BesselI[ 1, Sqrt[s mu/rhoc] rc] Ze[s_,mu_:4.0 Pi 10^-7, rc_:0.0203454,rhoc_:8.82573*10^-8,rhosolo_:100.0] := s mu/(2 Pi) Log[2*(15.0+ Sqrt[rhosolo/(s mu)]/rc] Zserie[s_]:=Ze[s]+zint[s]; Y[s_,e_:1/(36.0 Pi 10^9)]:=s 2 Pi e /(Log[2*15.0/rf]) A[s_]:=Exp[Sqrt[Zserie[s]*Y[s]]*-10000.0] (* from the graphic one can see that this funciton is bounded and goes to zero as s goes to either I*Infinity or -I*Infinity *) a[t_]:=2/Pi NIntegrate[Im[A[I 2 Pi x]/(2 Pi x) Cos[ 2 Pi x t], {x,0,\[Infinity]}, MaxRecursion -> 50, Method->Oscillatory] The error message did not help much for my case "Numerical integration stopping due to loss of precision. Achieved neither the requested PrecisionGoal nor AccuracyGoal; suspect one of the following: highly oscillatory integrand or the true value of the integral is 0. If your integrand is oscillatory try using the option Method->Oscillatory in NIntegrate.