Canuto, C.; Quarteroni, A. Spectral and pseudo-spectral methods for parabolic problems with non periodic boundary conditions. (English) Zbl 0485.65078 Calcolo 18, 197-217 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 21 Documents MSC: 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 35K20 Initial-boundary value problems for second-order parabolic equations Keywords:advection-diffusion equation; pseudo-spectral methods; stability; convergence; energy estimates; spectral Galerkin method; collocation; Gauss-Lobatto quadrature PDF BibTeX XML Cite \textit{C. Canuto} and \textit{A. Quarteroni}, Calcolo 18, 197--217 (1981; Zbl 0485.65078) Full Text: DOI References: [1] C. Canuto, A. Quarteroni,Approximation results for orthogonal polynomials in Sobolev spaces, Math. Comp. (1982) to appear. · Zbl 0567.41008 [2] C. Canuto, A. Quarteroni,Error estimates for spectral and pseudo-spectral approximations of hyperbolic equations, SIAM J. Numer. Anal. (1982), to appear. · Zbl 0508.65054 [3] P. J. Davis, P. Rabinowitz,Methods of Numerical Integration (1975), Academic Press, New York. · Zbl 0304.65016 [4] D. Gottlieb,The stability of the pseudo-spectral Chebyshev methods, ICASE Report 79-17, Institute for Computer Applications in Science and Engineering, Hampton, VA, 1979. · Zbl 0421.70030 [5] D. Gottlieb, S. A. Orszag,Numerical Analysis of Spectral Methods: Theory and Applications CBMS Regional Conference Series in Applied Mathematics 26, SIAM, Philadelphia, 1977. · Zbl 0412.65058 [6] J. Lions, E. Magenes,Non Homogeneous Boundary Value Problems and applications (1972),1, Springer Verlag, Berlin-Heidelberg-New York. · Zbl 0227.35001 [7] H. O. Kreiss, J. Oliger,Stability of the Fourier method, SIAM, J. Numer. Anal.,16, (1979), 421–433. · Zbl 0419.65076 · doi:10.1137/0716035 [8] Y. Maday, A. Quarteroni,Legendre and Chebyshev spectral approximations of Burgers’ equation, Numer. Math., 37 (1981), 321–332. · Zbl 0452.41007 · doi:10.1007/BF01400311 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.