Chebyshev and Fourier Spectral Methods: Second Revised Edition
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
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accuracy advection algebraic algorithm aliasing amplitude apply approximation asymptotic basis functions basis set boundary conditions boundary value problem Boyd calculation cardinal functions Chapter Chebyshev functions Chebyshev polynomials Chebyshev series coefﬁcients collocation compute constant convergence coordinate cosine decay deﬁned Deﬁnition degree denote differential equation difﬁculty discretization efﬁcient eigenfunctions eigenproblem eigenvalues endpoints evaluate exact solution example expansion exponentially factor fast ﬁlter finite ﬁnite difference ﬁnite element ﬁrst ﬂow Fourier coefﬁcients Fourier series Galerkin method Gaussian Gaussian quadrature Gegenbauer polynomials grid point values Hermite functions inﬁnite integration interval iteration Legendre polynomials linear mapping matrix modes multiple nonlinear numerical operator Orszag orthogonal oscillations parameter parity Physics poles pseudospectral method quadrature rational Chebyshev functions schemes second order semi-Lagrangian sine singularities slow manifold solve spatial spectral coefﬁcients spectral elements spectral methods spectral series spherical harmonics step strategy sufﬁciently symmetric Theorem time-marching tion transform trigonometric usually vector wavenumber waves zero