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Derivative-free high-order uniformly accurate schemes for highly oscillatory systems
IMA Journal of Numerical Analysis ( IF 2.1 ) Pub Date : 2021-02-18 , DOI: 10.1093/imanum/drab014
Philippe Chartier 1 , Mohammed Lemou 1 , Florian Méhats 1 , Xiaofei Zhao 2
Affiliation  

In this paper we address the computational aspects of uniformly accurate numerical methods for solving highly oscillatory evolution equations. In particular, we introduce an approximation strategy that allows the construction of arbitrary high-order methods using solely the right-hand side of the differential equation. No derivative of the vector field is required, while uniform accuracy is retained. The strategy is then applied to two different formulations of the problem, namely the two-scale and the micro–macro formulations. Numerical experiments on the Hénon–Heiles system, as well as on the Klein–Gordon equation and a Vlasov-type problem, confirm the validity of the new strategy.

中文翻译:

高振荡系统的无导高阶均匀精确方案

在本文中,我们解决了用于求解高度振荡演化方程的一致精确数值方法的计算方面。特别是,我们引入了一种近似策略,该策略允许仅使用微分方程的右侧构建任意高阶方法。不需要矢量场的导数,同时保持一致的精度。然后将该策略应用于问题的两种不同表述,即两尺度表述和微观宏观表述。Hénon-Heiles 系统以及 Klein-Gordon 方程和 Vlasov 型问题的数值实验证实了新策略的有效性。
更新日期:2021-02-18
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