Boyd, John P. Chebyshev and Fourier spectral methods. 2nd rev. ed. (English) Zbl 0994.65128 Mineola, NY: Dover Publications. xvi, 668 p. (2001). [For the first edition (1989) see Zbl 0681.65079.]In 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. Reviewer: Wilhelm Heinrichs (Essen) Cited in 3 ReviewsCited in 841 Documents MSC: 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 35-04 Software, source code, etc. for problems pertaining to partial differential equations Keywords:eigenvalue; aliasing; spectral blocking; slow manifold; nonlinear Galerkin theory; semi-Lagrangian spectral methods; textbook; Hermite function; Laguerre function; rational Chebyshev; function; sinc function; Galerkin method; spectral methods; spherical harmonic functions; collocation methods; convergence; interpolation; pseudospectral methods; time-integration methods; domain decomposition method; Newton-Kantorovich method; eigenvalue problems; continued method Citations:Zbl 0681.65079 PDFBibTeX XMLCite \textit{J. P. Boyd}, Chebyshev and Fourier spectral methods. 2nd rev. ed. Mineola, NY: Dover Publications (2001; Zbl 0994.65128)