The semigroup stability of the difference approximations for initialboundary value problems
Author:
Lixin Wu
Journal:
Math. Comp. 64 (1995), 7188
MSC:
Primary 65N06; Secondary 34G10, 65N12
MathSciNet review:
1257582
Fulltext PDF Free Access
Abstract 
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Abstract: For semidiscrete approximations and onestep fully discretized approximations of the initialboundary value problem for linear hyperbolic equations with diagonalizable coefficient matrices, we prove that the Kreiss condition is a sufficient condition for the semigroup stability (or stability). Also, we show that the stability of a fully discretized approximation generated by a locally stable RungeKutta method is determined by the stability of the semidiscrete approximation.
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 M. S. Agronovich, Theorem of matrices depending on parameters and its application to hyperbolic systems, Functional Anal. Appl. 6 (1972), 8593.
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 M. Goldberg and E. Tadmor, Schemeindependent stability criteria for difference approximations of hyperbolic initialboundary value problems. II, Math. Comp. 36 (1981), 603626. MR 606519 (83f:65142)
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 B. Gustafsson, H.O. Kreiss, and A. Sundström, Stability theory of difference approximations for mixed initial boundary value problems. II, Math. Comp. 26 (1972), 649686. MR 0341888 (49:6634)
 [5]
 R. Hersch, Mixed problems in several variables. J. Math. Mech. 12 (1963), 317334. MR 0147790 (26:5304)
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 , Stability theory for difference approximations of mixed initial boundary value problems. I, Math. Comp. 22 (1968), 703714. MR 0241010 (39:2355)
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 D. Michelson, Stability theory of difference approximations for multidimensional initial boundary value problems, Math. Comp. 40 (1983), 146. MR 679433 (84d:65068)
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 S. Osher, Systems of difference equations with general homogeneous boundary conditions, Trans. Amer. Math. Soc. 137 (1969), 171201. MR 0237982 (38:6259)
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 J. Rauch, is a continuable condition for Kreiss' mixed problems, Comm. Pure Appl. Math. 25 (1972), 6269. MR 0298232 (45:7284)
 [15]
 J. Strikwerda, Initial boundary value problems for the methods of lines, J. Comput. Phys. 34 (1980), 94107. MR 558146 (81d:65055)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718199512575826
PII:
S 00255718(1995)12575826
Keywords:
Hyperbolic,
semigroup stability,
RungeKutta methods
Article copyright:
© Copyright 1995
American Mathematical Society
