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.
Author(s): David Gottlieb, Steven A. Orszag
Series: CBMS-NSF Regional Conference Series in Applied Mathematics
Edition: SIAM
Publisher: Society for Industrial Mathematics
Year: 1987
Language: English
Pages: 179
Numerical Analysis of Spectral Methods:Theory and Applications......Page 1
Contents......Page 5
Preface......Page 7
SECTION 1 Introduction......Page 9
SECTION 2 Spectral Methods......Page 15
SECTION 3 Survey of Approximation Theory......Page 29
SECTION 4 Review of Convergence Theory......Page 55
SECTION 5 Algebraic Stability......Page 63
SECTION 6 Spectral Methods Using Fourier Series......Page 69
SECTION 7 Applications of Algebraic-Stability Analysis......Page 87
SECTION 8 Constant Coefficient Hyperbolic Equations......Page 97
SECTION 9 Time Differencing......Page 111
SECTION 10 Efficient Implementation of Spectral Methods......Page 125
SECTION 11 Numerical Results for Hyperbolic Problems......Page 129
SECTION 12 Advection-Diffusion Equation......Page 147
SECTION 13 Models of Incompressible Fluid Dynamics......Page 151
SECTION 14 Miscellaneous Applications of Spectral Methods......Page 157
SECTION 15 Survey of Spectral Methods and Applications......Page 163
APPENDIX Properties of Chebyshev Polynomial Expansions......Page 167
References......Page 171
Bibliography......Page 172
Index......Page 176
