Numerical Methods for Laplace Transform Inversion

Alan M. Cohen (auth.)0387282610, 9780387282619, 9780387688558, 0387688552

Operational methods have been used for over a century to solve many problems—for example, ordinary and partial differential equations. In many problems it is fairly easy to obtain the Laplace transform, but it can be very demanding to determine the inverse Laplace transform that is the solution of the given problem. Sometimes, after some difficult contour integration, we find that a series solution results, but even this may be quite difficult to evaluate in order to get an answer at a particular time value.

The advent of computers has given an impetus to developing numerical methods for the determination of the inverse Laplace transform. This book gives background material on the theory of Laplace transforms together with a comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms.

Audience

This book is intended for engineers, scientists, mathematicians, statisticians and financial planners.

Table of contents :
Front Matter….Pages I-XIV
Basic Results….Pages 1-22
Inversion Formulae and Practical Results….Pages 23-44
The Method of Series Expansion….Pages 45-70
Quadrature Methods….Pages 71-101
Rational Approximation Methods….Pages 103-120
The Method of Talbot….Pages 121-139
Methods based on the Post-Widder Inversion Formula….Pages 141-146
The Method of Regularization….Pages 147-155
Survey Results….Pages 157-168
Applications….Pages 169-196
Appendix….Pages 197-229
Back Matter….Pages 231-251