A Practical Guide to Pseudospectral Methods

by Bengt Fornberg

Overview

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.

Product Details

ISBN-13:	9780521645645
Publisher:	Cambridge University Press
Publication date:	10/28/1998
Series:	Cambridge Monographs on Applied and Computational Mathematics , #1
Edition description:	REPRINT
Pages:	244
Product dimensions:	5.94(w) x 8.98(h) x 0.51(d)

Table of Contents

1. Introduction; 2. Introduction to spectral methods via orthogonal functions; 3. Introduction to PS methods via finite differences; 4. Key properties of PS approximations; 5. PS variations/enhancements; 6. PS methods in polar and spherical geometries; 7. Comparisons of computational cost - FD vs. PS methods; 8. Some application areas for spectral methods; Appendices.

Editorial Reviews

"...an excellent introduction for someone who wants to understand the general theory of pseudospectral methods or their relationship to finite differences....meteorologists will want to own it because of its deep insight, abundant tables and aids to the programmer, and discussion of some topics not available in other books." John P. Boyd, Bulletin of the American Meteorological Society

"...this is a complementary work to be set alongside the standard texts on spectral methods....it stands alone as the handbook on implementing PS methods....It serves as an essential addition to the small library of books and monographs on spectral and PS methods. In particular it provides a unique perspective on PS methods, which equips the reader with an additional framework for developing a greater understanding of the subject and the means to quickly get hands dirty with some numerical programming using PS methods." Lawrence Mulholland, Mathematical Reviews

"Practical Guide to Pseudospectral Methods should be of reference use to researchers working in the area of pseudospectral methods." M.M. Gupta, Applied Mechanics Review

From the Publisher