Convenient stability criteria for difference approximations of hyperbolic initialboundary value problems. II
Authors:
Moshe Goldberg and Eitan Tadmor
Journal:
Math. Comp. 48 (1987), 503520
MSC:
Primary 65M10
MathSciNet review:
878687
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Abstract: The purpose of this paper is to extend the results of [4] in order to achieve more versatile, convenient stability criteria for a wide class of finitedifference approximations to initialboundary value problems associated with the hyperbolic system in the quarter plane , . With these criteria, stability is easily established for a large number of examples, where many of the cases studied in the recent literature are included and generalized.
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Goldberg and Eitan
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Goldberg and Eitan
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for difference approximations of hyperbolic initialboundary value
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36 (1981), no. 154, 603–626. MR 606519
(83f:65142), http://dx.doi.org/10.1090/S00255718198106065199
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Moshe
Goldberg and Eitan
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(1985), no. 170, 361–377. MR 777269
(86k:65078), http://dx.doi.org/10.1090/S00255718198507772697
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Sundström, Stability theory of difference
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Stanley
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G. Sköllermo, How the Boundary Conditions Affect the Stability and Accuracy of Some Methods for Hyperbolic Equations, Report No. 62, Dept. of Computer Science, Uppsala University, Uppsala, Sweden, 1975.
 [13]
G. Sköllermo, Error Analysis for the Mixed Initial Boundary Value Problem for Hyperbolic Equations, Report No. 63, Dept. of Computer Science, Uppsala University, Uppsala, Sweden, 1975.
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E. Tadmor, SchemeIndependent Stability Criteria for Difference Approximations to Hyperbolic initialBoundary Value Systems, Ph.D. thesis, Dept. of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel, 1978.
 [15]
L. N. Trefethen, Wave Propagation and Stability for Finite Difference Schemes, Ph.D. thesis, Report No. STANCS82905, Computer Science Department, Stanford University, Stanford, California, 1982.
 [1]
 M. Goldberg, "On a boundary extrapolation theorem by Kreiss," Math. Comp., v. 31, 1977, pp. 469477. MR 0443363 (56:1733)
 [2]
 M. Goldberg & E. Tadmor, "Schemeindependent stability criteria for difference approximations of hyperbolic initialboundary value problems. I," Math. Comp., v. 32, 1978, pp. 10971107. MR 501998 (80a:65196)
 [3]
 M. Goldberg & E. Tadmor, "Schemeindependent stability criteria for difference approximations of hyperbolic initialboundary value problems. II," Math. Comp., v. 36, 1981, pp. 603626. MR 606519 (83f:65142)
 [4]
 M. Goldberg & E. Tadmor, "Convenient stability criteria for difference approximations of hyperbolic initialboundary value problems," Math. Comp., v. 44, 1985, pp. 361377. MR 777269 (86k:65078)
 [5]
 B. Gustafsson, H.O. Kreiss & A. Sundström, "Stability theory of difference approximations for mixed initial boundary value problems. II," Math. Comp., v. 26, 1972, pp. 649686. MR 0341888 (49:6634)
 [6]
 B. Gustafsson & J. Oliger, "Stable boundary approximations for implicit time discretizations for gas dynamics," SIAM J. Sci. Statist. Comput., v. 3, 1982, pp. 408421. MR 677095 (84c:65151)
 [7]
 H.O. Kreiss, "Difference approximations for hyperbolic differential equations," in Numerical Solutions of Partial Differential Equations (J. H. Bramble, ed.), Academic Press, New York, 1966, pp. 5158. MR 0207223 (34:7039)
 [8]
 H.O. Kreiss & J. Oliger, Methods for the Approximate Solution of Time Dependent Problems, GARP Publication Series No. 10, Geneva, 1973.
 [9]
 J. Oliger, "Fourth order difference methods for the initial boundaryvalue problem for hyperbolic equations," Math. Comp., v. 28, 1974, pp. 1525. MR 0359344 (50:11798)
 [10]
 S. Osher, "Systems of difference equations with general homogeneous boundary conditions," Trans. Amer. Math. Soc., v. 137, 1969, pp. 177201. MR 0237982 (38:6259)
 [11]
 S. Osher, "Stability of parabolic difference approximations to certain mixed initialboundary value problems," Math. Comp., v. 26, 1972, pp. 1339. MR 0298990 (45:8039)
 [12]
 G. Sköllermo, How the Boundary Conditions Affect the Stability and Accuracy of Some Methods for Hyperbolic Equations, Report No. 62, Dept. of Computer Science, Uppsala University, Uppsala, Sweden, 1975.
 [13]
 G. Sköllermo, Error Analysis for the Mixed Initial Boundary Value Problem for Hyperbolic Equations, Report No. 63, Dept. of Computer Science, Uppsala University, Uppsala, Sweden, 1975.
 [14]
 E. Tadmor, SchemeIndependent Stability Criteria for Difference Approximations to Hyperbolic initialBoundary Value Systems, Ph.D. thesis, Dept. of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel, 1978.
 [15]
 L. N. Trefethen, Wave Propagation and Stability for Finite Difference Schemes, Ph.D. thesis, Report No. STANCS82905, Computer Science Department, Stanford University, Stanford, California, 1982.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198708786870
PII:
S 00255718(1987)08786870
Article copyright:
© Copyright 1987 American Mathematical Society
