Numerical methods for Laplace transform inversion
Información General
- Autores: Alan M. Cohen
- Editores: New York : Springer, [2007
- Año de publicación: 2007
- País: Estados Unidos
- Idioma: inglés
- ISBN: 0-387-28261-0, 978-0-387-28261-9, 978-0-387-68855-8
- Texto completo no disponible (Saber más ...)
Resumen
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.
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Índice
Preface.- Acknowledgments.- Notation.- Basic Results.- Inversion Formulae and Practical Results.- The Method of Series Expansion.- Quadrature Methods.- Rational Approximation Methods.- The Method of Talbot.- Methods Based on the Post-Widder Inversion Formula.- The Method of Regularization.- Survey Results.- Applications.- Appendix.- Index.
