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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 $ {u_t} = A{u_x}$ in the quarter plane $ x \geqslant 0$, $ t \geqslant 0$. 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.


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DOI: https://doi.org/10.1090/S0025-5718-1978-0501998-X
Article copyright: © Copyright 1978 American Mathematical Society