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Stability and convergence of spectral methods for hyperbolic initial-boundary value problems
Author:
P. Dutt
Journal:
Math. Comp. 53 (1989), 547-561
MSC:
Primary 65M70; Secondary 65M12
MathSciNet review:
982366
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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.
- [1]
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.
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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.
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D. Gottlieb & S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, 1984.
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Heinz-Otto
Kreiss, Initial boundary value problems for hyperbolic
systems, Comm. Pure Appl. Math. 23 (1970),
277–298. MR 0437941
(55 #10862)
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Liviu
Lustman, The time evolution of spectral discretizations of
hyperbolic systems, SIAM J. Numer. Anal. 23 (1986),
no. 6, 1193–1198. MR 865950
(88a:35147), http://dx.doi.org/10.1137/0723080
- [6]
Jeffrey
Rauch, \𝑐𝑎𝑙𝐿₂ is a
continuable initial condition for Kreiss’ mixed problems, Comm.
Pure Appl. Math. 25 (1972), 265–285. MR 0298232
(45 #7284)
- [1]
- 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.
- [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.
- [3]
- D. Gottlieb & S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, 1984.
- [4]
- H. O. Kreiss, "Initial boundary value problems for hyperbolic systems," Comm. Pure Appl. Math., v. 23, 1970, pp. 277-298. MR 0437941 (55:10862)
- [5]
- L. Lustman, "The time evolution of spectral discretizations of hyperbolic systems," SIAM J. Numer. Anal. (To appear). MR 865950 (88a:35147)
- [6]
- J. Rauch, "
 is a continuable initial condition for Kreiss' mixed problems," Comm. Pure Appl. Math., v. 25, 1972, pp. 265-285. MR 0298232 (45:7284)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1989-0982366-0
PII:
S 0025-5718(1989)0982366-0
Keywords:
Initial-boundary value problems,
regularization,
convolution,
stability,
convergence
Article copyright:
© Copyright 1989 American Mathematical Society
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