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© 2007

Numerical Methods for Laplace Transform Inversion

Book

Part of the Numerical Methods and Algorithms book series (NUAL, volume 5)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Alan M. Cohen
    Pages 1-22
  3. Alan M. Cohen
    Pages 23-44
  4. Alan M. Cohen
    Pages 45-70
  5. Alan M. Cohen
    Pages 71-101
  6. Alan M. Cohen
    Pages 103-120
  7. Alan M. Cohen
    Pages 121-139
  8. Alan M. Cohen
    Pages 147-155
  9. Alan M. Cohen
    Pages 157-168
  10. Alan M. Cohen
    Pages 169-196
  11. Alan M. Cohen
    Pages 197-229
  12. Back Matter
    Pages 231-251

About this book

Introduction

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.

Keywords

Koordinatentransformation Laplace transform inversion Numerical methods differential equation integration numerical method partial differential equation

Authors and affiliations

  1. 1.Cardiff UniversityCardiff

Bibliographic information

Reviews

From the reviews:

"This book gives background material on the theory of Laplace transforms together with a comprehensive list of numerical methods for determination of the inverse Laplace transform. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms. It provides a balanced course of Laplace transforms consisting of theory, numerical techniques and applications. … This book may be a useful tool for all those who use Laplace transforms in their work whether they are mathematicians, engineers or financial planners." (Som Prakash Goyal, Zentralblatt MATH, Vol. 1127 (4), 2008)

"In this book, Alan M. Cohen summarizes known results related to numerical methods. The book starts with basic analytic theory of the Laplace transform. … The book provides a large amount of carefully selected and clearly explained examples, and seems to be ideal for self-study or preparing students’ courses for different levels. By gathering various information on the Laplace transform in one place, the author has created a standard reference source." (Alexander Denisjuk, Mathematical Reviews, Issue 2009 c)