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Numerical Analysis of Spectral Methods: Theory and ApplicationsNumerical Analysis of Spectral Methods: Theory and Applications

David Gottlieb and Steven A. Orszag



CBMS-NSF Regional Conference Series in Applied Mathematics 26

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

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.

1977 / v + 170 pages / Softcover / ISBN-13: 978-0-898710-23-6 / ISBN-10: 0-89871-023-5 /
List Price $97.00 / SIAM/CBMS Member Price $60.90 / Order Code CB26
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