Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. I

Authors:
Moshe Goldberg and Eitan Tadmor

Journal:
Math. Comp. **32** (1978), 1097-1107

MSC:
Primary 65M10

DOI:
https://doi.org/10.1090/S0025-5718-1978-0501998-X

MathSciNet review:
501998

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Abstract: Easily checkable sufficient stability criteria are obtained for explicit dissipative approximations to mixed initial-boundary value problems associated with the system in the quarter plane , . The criteria are given entirely in terms of the boundary conditions for the outflow unknowns. The results imply that certain well-known boundary conditions, when used in combination with any (stable) dissipative scheme, always maintain stability.

**[1]**M. GOLDBERG, "On a boundary extrapolation theorem by Kreiss,"*Math. Comp.*, v. 31, 1977, pp. 469-477. MR**0443363 (56:1733)****[2]**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)****[3]**H.-O. KREISS, "Difference approximations for hyperbolic differential equations,"*Numerical Solution of Partial Differential Equations*(Proc. Sympos., Univ. of Maryland, College Park, Maryland, 1965), Academic Press, New York, 1966, pp. 51-58. MR**0207223 (34:7039)****[4]**H.-O.KREISS, "Stability theory for difference approximations of mixed initial boundary value problems. I,"*Math. Comp.*, v. 22, 1968, pp. 703-714. MR**39**#2355. MR**0241010 (39:2355)****[5]**G. SKÖLLERMO,*How the Boundary Conditions Affect the Stability and Accuracy of Some Implicit Methods for Hyperbolic Equations*, Report #62, 1975, Dept. of Computer Science, Uppsala University.

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DOI:
https://doi.org/10.1090/S0025-5718-1978-0501998-X

Article copyright:
© Copyright 1978
American Mathematical Society