Numerical Analysis of Spectral Methods : Theory and Applications:Numerical Analysis of Spectral Methods : Theory and Applications (CBMS-NSF Regional Conference Series in Applied Mathematics) (CBMS-NSF Regional Conference Series in Applied Mathematics)
By David Gottlieb, Steven A. Orszag
Publisher: Society for Industrial Mathematics
Number Of Pages: 176
Publication Date: 1987-01-01
ISBN-10 / ASIN: 0898710235
ISBN-13 / EAN: 9780898710236
Binding: Paperback
A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.
Contents
Preface v
Section 1
INTRODUCTION 1
Section 2
SPECTRAL METHODS 7
Section 3
SURVEY OF APPROXIMATION THEORY 21
Section 4
REVIEW OF CONVERGENCE THEORY 47
Section 5
ALGEBRAIC STABILITY 55
Section 6
SPECTRAL METHODS USING FOURIER SERIES 61
Section 7
APPLICATIONS OF ALGEBRAIC-STABILITY ANALYSIS 79
Section 8
CONSTANT COEFFICIENT HYPERBOLIC EQUATIONS 89
Section 9
TIME DIFFERENCING 103
Section 10
EFFICIENT IMPLEMENTATION OF SPECTRAL METHODS . . . . 117
Section 11
NUMERICAL RESULTS FOR HYPERBOLIC PROBLEMS 121
Section 12
ADVECTION-DIFFUSION EQUATION 139
Section 13
MODELS OF INCOMPRESSIBLE FLUID DYNAMICS 143
Section 14
MISCELLANEOUS APPLICATIONS OF SPECTRAL METHODS 149
Section 15
SURVEY OF SPECTRAL METHODS AND APPLICATIONS . . . . 155
Appendix
PROPERTIES OF CHEBYSHEV POLYNOMIAL EXPANSIONS . . 159
PROPERTIES OF LEGENDRE POLYNOMIAL EXPANSIONS . . . 162
References 163
Bibliography 164
Index 168
Numerical Analysis of Spectral Methods Theory and Applications.part2
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Numerical Analysis of Spectral Methods Theory and Applications.part1
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Numerical Analysis of Spectral Methods
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Numerical Analysis of Spectral Methods : Theory and Applications: nn.jpg
