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