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.
Spectral MethodsSurvey of Approximation TheoryReview of Convergence TheoryAlgebraic StabilitySpectral Methods Using Fourier SeriesApplications of Algebraic Stability AnalysisConstant Coefficient Hyperbolic EquationsTime DifferencingEfficient Implementation of Spectral MethodsNumerical Results for Hyperbolic ProblemsAdvection-Diffusion EquationModels of Incompressible Fluid DynamicsMiscellaneous Applications of Spectral MethodsSurvey of Spectral Methods and ApplicationsProperties of Chebyshev and Legendre Polynomial Expansions.