目录
- Chapter 1 Preliminaries
1.1 Some basic ideas of spectral methods
1.2 Orthogonal polynomials
1.3 Chebyshev and Legendre polynomials
1.4 Jacobi polynomials and generalized Jacobi polynomials
1.5 Fast Fourier transform
1.6 Several popular time discretization methods
1.7 Iterative methods and preconditioning
1.8 Error estimates of polynomial approximations
Chapter 2 Spectral-Collocation Methods
2.1 Differentiation matrices for polynomial basis functions
2.2 Differentiation matrices for Fourier collocation methods
2.3 Eigenvalues of Chebyshev collocation operators
2.4 Chebyshev collocation method for two-point BVPs
2.5 Collocation method in the weak form and preconditioning
Chapter 3 Spectral-Galerkin Methods
3.1 General setup
3.2 Legendre-Galerkin method
3.3 Chebyshev-Galerkin method
3.4 Chebyshev-Legendre Galerkin method
3.5 Preconditioned iterative method
3.6 Spectral-Galerkin methods for higher-order equations
3.7 Error estimates
Chapter 4 Spectral Methods in Unbounded Domains
4.1 Hermite spectral methods
4.2 Laguerre spectral methods
4.3 Spectral methods using rational functions
4.4 Error estimates in unbounded domains
Chapter 5 Some applications in one space dimension
5.1 Pseudospectral methods for boundary layer problems
5.2 Pseudospectral methods for Fredholm integral equations
5.3 Chebyshev spectral methods for parabolic equations
5.4 Fourier spectral methods for the KdV equation
5.5 Fourier method and filters
5.6 Essentially non-oscillatory spectral schemes
Chapter 6 Spectral methods in Multi-dimensional Domains
6.1 Spectral-collocation methods in rectangular domains
6.2 Spectral-Galerkin methods in rectangular domains
6.3 Spectral-Galerkin methods in cylindricaldomains
6.4 A fast Poisson Solver using finite differences
Chapter 7 Some applications in multi-dimensions
7.1 Spectral methods for wave equations
7.2 Laguerre-Hermite method for Schrödinger equations
7.3 Spectral approximation of the Stokes equations
7.4 Spectral-projection method for Navier-Stokes equations
7.5 Axisymmetric flows in a cylinder
Appendix A Some online software
A.1 MATLAB Differentiation Matrix Suite
A.2 PseudoPack
Bibliography
Index
京公网安备 11010102004214号