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arXiv · 1712.06371

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

Philippe Chartier·Mohammed Lemou·Florian Méhats·Gilles Vilmart
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Abstract

We introduce a new methodology to design uniformly accurate methods for oscillatory 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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Philippe Chartier, Mohammed Lemou, Florian Méhats, Gilles Vilmart. 2017-12-18. A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations. https://arxiv.org/abs/1712.06371

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