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Re: Laplace transform

• To: MathGroup at yoda.physics.unc.edu
• Subject: Re: Laplace transform
• From: Cetin Cetinkaya <cetin at acm0.me.uiuc.edu>
• Date: Wed, 25 May 1994 22:29:16 -0500

Michael Buschmann <mike at mem.unibe.ch> wrote:

>I would like to numerically invert a Laplace transform.
>Simple-minded use of NIntegrate of the inversion integral
>gives incorrect and nonconvergent values. Any ideas ?

The standart way of doing this is to use a FFT scheme. The
only motification you need to do is to replace s (Laplace 
variable) with j w  where j=Sqrt[-1] and w is angular 
frequency. 
Two important points to pay attention:
1- Sampling rate: This should depends of the nature of your 
   function. 
2- Damping: In order to utilize FFT, your signal should die
   out at "infinity". Adding moderate amount of damping would
   help to "mimic" this condition. It should not effect the 
   final results much.
A good book on this issue is The Fast Fourier Transform and
its Applications by E.O. Brigham. This book is a nice introduction
with many applications.
For the application of FFT using MATHEMATICA, you would want to
check with Mathematica for the Sciences by R. E. Crandall. 
Section 8.2 (pp. 217-232) offers a number of nice applications and
some usefull hints.

I hope that this would help. 

Cetin Cetinkaya