Vichnevetsky, Robert; Bowles, John B. [Birkhoff, Garrett] Fourier analysis of numerical approximations of hyperbolic equations. With a foreword by Garrett Birkhoff. (English) Zbl 0495.65041 SIAM Studies in Applied Mathematics, 5. Philadelphia: SIAM - Society for Industrial and Applied Mathematics. (Distr. by John Wiley & Sons). XII, 140 p. $ 21.50; £13.00 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 189 Documents MSC: 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 35L15 Initial value problems for second-order hyperbolic equations 35L45 Initial value problems for first-order hyperbolic systems 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 65T40 Numerical methods for trigonometric approximation and interpolation 65G50 Roundoff error Keywords:Fourier methods; discrete Fourier transform; semidiscretization methods; damping; diffusion; filtering; group velocity; time-Fourier transforms; norm of the global error; spectral methods PDFBibTeX XML