Numerical analysis of spectral methods theory and applications - Gottlieb, David (Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1977)
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Includes bibliographical references
Spectral methods -- Survey of approximation theory -- Review of convergence theory -- Algebraic stability -- Spectral methods using Fourier series -- Applications of algebraic stability analysis -- Constant coefficient hyperbolic equations -- time differencing -- Efficient implementation of spectral methods -- Numerical results for hyperbolic problems -- Advection-diffusion equation -- Models of incompressible fluid dynamics -- Miscellaneous applications of spectral methods -- Survey of spectral methods and applications -- Properties of Chebyshev and Legendre polynomial expansions
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