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

Goldberg, Moshe; Tadmor, Eitan

doi:10.1090/S0025-5718-1987-0878687-0

Convenient 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. 48 (1987), 503-520 Request permission

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 ${{\mathbf {u}}_t} = A{{\mathbf {u}}_x} + B{\mathbf {u}} + {\mathbf {f}}$ in the quarter plane $x \geqslant 0$, $t \geqslant 0$. 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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