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

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P. Chartier, M. Lemou, F. Méhats, and G. 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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Key Words. highly-oscillatory problems, stroboscopic averaging, standard averaging, micro-macro method, pullback method, uniform accuracy.

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