Scheme-independent stability criteria for difference approximations of hyperbolic initial-boundary value problems. II
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- by Moshe Goldberg and Eitan Tadmor PDF
- Math. Comp. 36 (1981), 603-626 Request permission
Abstract:
Convenient stability criteria are obtained for difference approximations to initial-boundary value problems associated with the hyperbolic system ${{\mathbf {u}}_t} = A{{\mathbf {u}}_x} + B{\mathbf {u}} + {\mathbf {f}}$ in the quarter plane $x \geqslant 0$, $t \geqslant 0$. The approximations consist of arbitrary basic schemes and a wide class of boundary conditions. The new criteria are given in terms of the outflow part of the boundary conditions and are independent of the basic scheme. The results easily imply that a number of well-known boundary treatments, when used in combination with arbitrary stable basic schemes, always maintain stability. Consequently, many special cases studied in recent literature are generalized.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Math. Comp. 36 (1981), 603-626
- MSC: Primary 65M10
- DOI: https://doi.org/10.1090/S0025-5718-1981-0606519-9
- MathSciNet review: 606519