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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.

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
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