On the strong stability of finite difference schemes for hyperbolic systems in two space dimensions
نویسنده
چکیده
We study the stability of some finite difference schemes for symmetric hyperbolic systems in two space dimensions. For the so-called upwind scheme and the Lax-Wendroff scheme with a stabilizer, we show that stability is equivalent to strong stability, meaning that both schemes are either unstable or `-decreasing. These results improve on a series of partial results on strong stability. We also show that, for the Lax-Wendroff scheme without stabilizer, strong stability may not occur no matter how small the CFL parameters are chosen. This partially invalidates some of Turkel’s conjectures in [12]. AMS subject classification: 65M12, 65M06, 35L45.
منابع مشابه
Stability of finite difference schemes for hyperbolic systems in two space dimensions
We study the stability of some finite difference schemes for hyperbolic systems in two space dimensions. The grid is assumed to be cartesian, but the space steps in each direction are not necessarily equal. Our sufficient stability conditions are shown to be also necessary for one concrete example. We conclude with some numerical illustrations of our result. AMS subject classification: 65M12, 6...
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