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

Goldberg, Moshe; Tadmor, Eitan

doi:10.1090/S0025-5718-1985-0777269-7

Convenient stability criteria for difference approximations of hyperbolic initial-boundary value problems
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by Moshe Goldberg and Eitan Tadmor PDF

Math. Comp. 44 (1985), 361-377 Request permission

Abstract:

New convenient stability criteria are provided in this paper for a large 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 $x \geqslant 0$, $t \geqslant 0$. Using the new criteria, stability is easily established for numerous combinations of well-known basic schemes and boundary conditions, thus generalizing many special cases studied in the recent literature.

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