Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems. II

Authors:
Moshe Goldberg and Eitan Tadmor

Journal:
Math. Comp. **48** (1987), 503-520

MSC:
Primary 65M10

DOI:
https://doi.org/10.1090/S0025-5718-1987-0878687-0

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 finite-difference approximations to initial-boundary 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.

**[1]**M. Goldberg, "On a boundary extrapolation theorem by Kreiss,"*Math. Comp.*, v. 31, 1977, pp. 469-477. MR**0443363 (56:1733)****[2]**M. Goldberg & E. Tadmor, "Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. I,"*Math. Comp.*, v. 32, 1978, pp. 1097-1107. MR**501998 (80a:65196)****[3]**M. Goldberg & E. Tadmor, "Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. II,"*Math. Comp.*, v. 36, 1981, pp. 603-626. MR**606519 (83f:65142)****[4]**M. Goldberg & E. Tadmor, "Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems,"*Math. Comp.*, v. 44, 1985, pp. 361-377. 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. 649-686. 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. 408-421. 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. 51-58. 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 boundary-value problem for hyperbolic equations,"*Math. Comp.*, v. 28, 1974, pp. 15-25. MR**0359344 (50:11798)****[10]**S. Osher, "Systems of difference equations with general homogeneous boundary conditions,"*Trans. Amer. Math. Soc.*, v. 137, 1969, pp. 177-201. MR**0237982 (38:6259)****[11]**S. Osher, "Stability of parabolic difference approximations to certain mixed initial-boundary value problems,"*Math. Comp.*, v. 26, 1972, pp. 13-39. 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,*Scheme-Independent Stability Criteria for Difference Approximations to Hyperbolic initial-Boundary 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. STAN-CS-82-905, Computer Science Department, Stanford University, Stanford, California, 1982.

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DOI:
https://doi.org/10.1090/S0025-5718-1987-0878687-0

Article copyright:
© Copyright 1987
American Mathematical Society