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MathGroup Archive 2004

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Re:A NIntegrate question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52062] Re:[mg52029] A NIntegrate question
  • From: Anton Antonov <antonov at wolfram.com>
  • Date: Tue, 9 Nov 2004 01:36:53 -0500 (EST)
  • References: <418F8696.9020906@wolfram.com>
  • Sender: owner-wri-mathgroup at wolfram.com

Dear Antonio Carlos Siqueira

Two of your inputs are incomplete:

(1) 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]

which I guess should be

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]

(2) 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]

which I guess should be

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]

Are these assumtions of mine correct?

Further, what is the Mathematica version you are running your 
computations with?
 For what values of t you are getting the NIntegrate message?

Anton Antonov,
Wolfram Research, Inc

> -------- Original Message --------
> Subject: [mg52062] [mg52029] A NIntegrate question
> Date: Sun, 7 Nov 2004 01:04:44 -0500 (EST)
> From: acsl at dee.ufrj.br (Antonio Carlos Siqueira)
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
>
> 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.
>


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