Numerical Analysis of Spectral Methods

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.

Spis treści:
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.