A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations

Philippe Chartier 1, 2 Mohammed Lemou 1, 2 Florian Méhats 1, 2 Gilles Vilmart 3, 4
2 MINGUS - Multi-scale numerical geometric schemes
IRMAR - Institut de Recherche Mathématique de Rennes, ENS Rennes - École normale supérieure - Rennes, Inria Rennes – Bretagne Atlantique
Abstract : We introduce a new methodology to design uniformly accurate methods for oscil-latory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-stiff to highly-oscillatory. Thanks to an averaging transformation, the stiffness of the problem is softened, allowing for standard schemes to retain their usual orders of convergence. Overall, high-order numerical approximations are obtained with errors and at a cost independent of the regime.
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Submitted on : Thursday, January 10, 2019 - 11:30:36 AM
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Philippe Chartier, Mohammed Lemou, Florian Méhats, Gilles Vilmart. A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations. Foundations of Computational Mathematics, Springer Verlag, In press, pp.1-29. ⟨10.1007/s10208-019-09413-3⟩. ⟨hal-01666472v2⟩

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