A Practical Guide to Pseudospectral Methods (Cambridge Monographs on Applied and Computational Mathematics)
Bengt Fornberg | 1996-01-26 00:00:00 | Cambridge University Press | 288 | Engineering
During the past two decades, pseudospectral methods have emerged as successful, and often superior, alternatives to better known computational procedures, such as finite difference and finite element methods of numerical solution, in several key application areas. These areas include computational fluid dynamics, wave motion, and weather forecasting. This book explains how, when and why this pseudospectral approach works. In order to make the subject accessible to students as well as researchers and engineers, the author presents the subject using illustrations, examples, heuristic explanations, and algorithms rather than rigorous theoretical arguments. This book will be of interest to graduate students, scientists, and engineers interested in applying pseudospectral methods to real problems.
Reviews
This book is a wonderful guide to pseudo-spectral techniques which begins its discussion as an extension or more precisely as the limit of finite difference techniques. Unfortunately for anyone who would wish to learn these techniques I would have to recomend another book. However, for someone who already knows these techniques then this book is invaluable. It covers in a clear, mathematical way in which certain pitfalls and problems may be overcome. It does not, however, teach more of the advanced methods that must be used in more complex boundary value problems.
I think that a mathematician will find this book easy reading. I also think that an educated engineer will also have little difficulty following along. I do not recomend this book to anyone who has not taken a course in PDE's as background theory is always more important to application than indiscriminately learning a technique.
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