Contractive difference schemes for symmetric hyperbolic systems
Authors:
Philip Brenner and Vidar Thomée
Journal:
Math. Comp. 25 (1971), 205217
MSC:
Primary 65N05
MathSciNet review:
0297151
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Abstract 
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Abstract: Consider the initialvalue problem for a constantcoefficient symmetric hyperbolic system with initialvalues vanishing in a halfspace. Consider also a finite difference operator consistent with the system. Conditions are given in terms of the orders of dissipation and accuracy which ensure that the solution of the discrete problem tends to zero exponentially with the meshwidth in halfspaces where the solution of the continuous problem vanishes.
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 Ph. Brenner & V. Thomée, "Stability and convergence rates in for certain difference schemes," Math. Scand., v. 27, 1970, pp. 523. MR 0278549 (43:4279)
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 Ph. Brenner & V. Thomée, "Estimates near discontinuities for some difference schemes," Math. Scand. (To appear.) MR 0305613 (46:4743)
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 S. Gerschgorin, "Über die Abgrenzung der Eigenwerte einer Matrix," Izv. Akad. Nauk SSSR, v. 7, 1931, pp. 749754.
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 B. Parlett, "Accuracy and dissipation in difference schemes," Comm. Pure Appl. Math., v. 19, 1966, pp. 111123. MR 33 #5141. MR 0196957 (33:5141)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197102971511
PII:
S 00255718(1971)02971511
Keywords:
Symmetric hyperbolic system,
initialvalue problem,
difference scheme,
contractive,
dissipative,
stability,
accuracy,
Fourier transform
Article copyright:
© Copyright 1971 American Mathematical Society
