Chebyshev and Fourier spectral methods. (Q2781419)

[For the first edition (1989) see Zbl 0681.65079.]NEWLINENEWLINENEWLINEIn the second edition the Chapter 11 (fluid computations) and Appendix G (least squares) are deleted. Four new chapters on eigenvalue problems, aliasing and spectral blocking, the slow manifold and nonlinear Galerkin theory, and semi-Lagrangian spectral methods are added. All chapters have been updated and most have been rewritten. Chapter 18 has several new sections on polar coordinates. Appendix E contains a new table giving the transformations of first and second derivatives for a two-dimensional map. Appendix F has new analytical formulas for the Legendre-Lobatto grid points up to nine-point grids, which is sufficient for most spectral element applications.