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Highly-oscillatory evolution equations with multiple frequencies: averaging and numerics

Philippe Chartier 1, 2, * Mohammed Lemou 3, 1, 2 Florian Méhats 1, 2
* Corresponding author
2 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : In this paper, we are concerned with the application of the recently introduced multi-revolution composition methods, on the one hand, and two-scale methods, on the other hand, to a class of highly-oscillatory evolution equations with multiple frequencies. The main idea relies on a well-balanced reformulation of the problem as an equivalent mono-frequency equation which allows for the use of the two aforementioned techniques.
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Philippe Chartier, Mohammed Lemou, Florian Méhats. Highly-oscillatory evolution equations with multiple frequencies: averaging and numerics. Numerische Mathematik, Springer Verlag, 2017, 136 (4), pp.907-939. ⟨10.1007/s00211-016-0864-4⟩. ⟨hal-01281950v2⟩

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