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Article Dans Une Revue IMA Journal of Numerical Analysis Année : 2023

Sharp stability for finite difference approximations of hyperbolic equations with boundary conditions

Résumé

In this article, we consider a class of finite rank perturbations of Toeplitz operators that have simple eigenvalues on the unit circle. Under a suitable assumption on the behavior of the essential spectrum, we show that such operators are power bounded. The problem originates in the approximation of hyperbolic partial differential equations with boundary conditions by means of finite difference schemes. Our result gives a positive answer to a conjecture by Trefethen, Kreiss and Wu that only a weak form of the so-called Uniform Kreiss-Lopatinskii Condition is sufficient to imply power boundedness.
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Dates et versions

hal-03131269 , version 1 (04-02-2021)

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Citer

Jean-François Coulombel, Grégory Faye. Sharp stability for finite difference approximations of hyperbolic equations with boundary conditions. IMA Journal of Numerical Analysis, 2023, 43 (1), pp.187-224. ⟨hal-03131269⟩
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