A Practical Guide to Pseudospectral Methods

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Cambridge University Press, Oct 28, 1998 - Mathematics - 231 pages
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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.
 

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Contents

Introduction to spectral methods via orthogonal functions
4
Introduction to PS methods via finite differences
14
Key properties of PS approximations
36
PS variations and enhancements
83
PS methods in polar and spherical geometries
101
Comparisons of computational cost for FD and
118
Applications for spectral methods
127
Appendices
153
B Tau Galerkin and collocation PS implementations
161
Codes for algorithm to find FD weights
167
E Potential function estimate for polynomial interpolation
173
G Stability domains for some ODE solvers
197
H Energy estimates
210
References
217
Index
229
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