Numerical Methods for Laplace Transform Inversion

Operational methods have been used for over a century to solve problems such as ordinary and partial differential equations. When solving such problems, in many cases it is fairly easy to obtain the Laplace transform, but very difficult to determine the inverse Laplace transform that is the solution of a given problem. Sometimes, after a difficult contour integration, we may find that a series solution results, but 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 fairly 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.

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.