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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Stability and convergence of spectral methods for hyperbolic initial-boundary value problems
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by P. Dutt PDF
Math. Comp. 53 (1989), 547-561 Request permission

Abstract:

In this paper we present a modified version of the pseudospectral method for solving initial-boundary value systems of hyperbolic partial differential equations. We are able to avoid problems of instability by regularizing the boundary conditions. We prove the stability and convergence of our proposed scheme and obtain error estimates.
References
    D. Gottlieb, L. Lustman & E. Tadmor, Stability Analysis of Spectral Methods for Hyperbolic Initial Boundary Value Systems, NASA Contractor Report No. 178041, ICASE Report No. 86-2. D. Gottlieb, L. Lustman & E. Tadmor, Convergence of Spectral Methods for Hyperbolic Initial Boundary Value Systems, NASA Contractor Report No. 178063, ICASE Report No. 86-8. D. Gottlieb & S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, 1984.
  • Heinz-Otto Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970), 277–298. MR 437941, DOI 10.1002/cpa.3160230304
  • Liviu Lustman, The time evolution of spectral discretizations of hyperbolic systems, SIAM J. Numer. Anal. 23 (1986), no. 6, 1193–1198. MR 865950, DOI 10.1137/0723080
  • Jeffrey Rauch, ${\cal L}_{2}$ is a continuable initial condition for Kreiss’ mixed problems, Comm. Pure Appl. Math. 25 (1972), 265–285. MR 298232, DOI 10.1002/cpa.3160250305
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 547-561
  • MSC: Primary 65M70; Secondary 65M12
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0982366-0
  • MathSciNet review: 982366