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The Exponential Accuracy of Fourier and Chebyshev Differencing Methods

1986; Society for Industrial and Applied Mathematics; Volume: 23; Issue: 1 Linguagem: Inglês

10.1137/0723001

1095-7170

Eitan Tadmor,

Mathematical functions and polynomials

Next article The Exponential Accuracy of Fourier and Chebyshev Differencing MethodsEitan TadmorEitan Tadmorhttps://doi.org/10.1137/0723001PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIt is shown that when differencing analytic functions using the pseudospectral Fourier or Chebyshev methods, the error committed decays to zero at an exponential rate.[1] C. Canuto and , A. Quarteroni, Approximation results for orthogonal polynomials in Sobolev spaces, Math. Comp., 38 (1982), 67–86 82m:41003 0567.41008 CrossrefISIGoogle Scholar[2] C. Canuto and , A. Quarteroni, Error estimates for spectral and pseudospectral approximations of hyperbolic equations, SIAM J. Numer. Anal., 19 (1982), 629–642 10.1137/0719044 83e:65183 0508.65054 LinkISIGoogle Scholar[3] P. Davis and , P. Rabinowitz, Methods of numerical integration, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers] New York-London, 1975xii+459 56:7119 0304.65016 Google Scholar[4] David Gottlieb, The stability of pseudospectral-Chebyshev methods, Math. Comp., 36 (1981), 107–118 82b:65123 0469.65076 CrossrefISIGoogle Scholar[5] David Gottlieb, , M. Hussaini and , S. Orszag, R. Voigt, , D. Gottlieb and , M. Hussaini, Theory and applications of spectral methodsSpectral methods for partial differential equations (Hampton, Va., 1982), SIAM, Philadelphia, PA, 1984, 1–54, Proc. 1982 NASA Langley Research Center Symposium 86h:65142 0599.65079 Google Scholar[6] David Gottlieb and , S. Orszag, Numerical analysis of spectral methods: theory and applications, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1977v+172, CBMS Regional Conference Series in Applied Mathematics, 26 58:24983 0412.65058 LinkGoogle Scholar[7] H. Kreiss and , J. 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Pasciak, Spectral and pseudospectral methods for advection equations, Math. Comp., 35 (1980), 1081–1092 81i:65073 0448.65071 CrossrefISIGoogle Scholar[13] A. Patera, A spectral element method for fluid dynamics: laminar flow in a channel expansion, J. Comput. Phys., 54 (1984), 468–488 10.1016/0021-9991(84)90128-1 0535.76035 CrossrefISIGoogle Scholar[14] L. Reyna, Stability of Chebyshev collocation, 1983, preprint, Courant Institute of Mathematical Sciences, New York Univ., New York Google Scholar[15] E. Tadmor, Finite-difference, spectral and Galerkin methods for time-dependent problems, ICASE Report, 83-22, NASA Langley Research Center, Hampton, VA, 1983, NASA CR-172149 Google Scholar[16] A. Zygmund, Trigonometric series: Vol. I, Second edition, reprinted with corrections and some additions, Cambridge University Press, London, 1968Vol. I. xiv+383 pp. 38:4882 Google ScholarKeywordsFourier approximationChebyshev approximationpseudospectral differencingexponential decay Next article FiguresRelatedReferencesCited ByDetails Modification of Chebyshev Pseudospectral Method to Minimize the Gibbs Oscillatory Behaviour in Resynthesizing ProcessCircuits, Systems, and Signal Processing, Vol. 41, No. 11 | 2 July 2022 Cross Ref Collocation‐based harmonic balance framework for highly accurate periodic solution of nonlinear dynamical systemInternational Journal for Numerical Methods in Engineering, Vol. 169 | 27 September 2022 Cross Ref Unsaturated Algorithms for the Numerical Solution of Elliptic Boundary Value Problems in Smooth Axisymmetric DomainsSiberian Advances in Mathematics, Vol. 32, No. 3 | 2 September 2022 Cross Ref Comparative analysis of post-processing on spectral 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