The semigroup stability of the difference approximations for initial-boundary value problems

Wu, Lixin

doi:10.1090/S0025-5718-1995-1257582-6

The semigroup stability of the difference approximations for initial-boundary value problems
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Math. Comp. 64 (1995), 71-88 Request permission

Abstract:

For semidiscrete approximations and one-step fully discretized approximations of the initial-boundary value problem for linear hyperbolic equations with diagonalizable coefficient matrices, we prove that the Kreiss condition is a sufficient condition for the semigroup stability (or ${l_2}$ stability). Also, we show that the stability of a fully discretized approximation generated by a locally stable Runge-Kutta method is determined by the stability of the semidiscrete approximation.

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Theorem of matrices depending on parameters and its application to hyperbolic systems

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