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Journal Articles Mathematical Methods in the Applied Sciences Year : 2015

Stroboscopic averaging of highly oscillatory nonlinear wave equations

Abstract

In this paper, we are concerned with stroboscopic averaging for highly oscillatory evolution equations posed in a Banach space. Using Taylor expansion, we construct a non-oscillatory high-order system whose solution remains exponentially close to the exact one over a long time. We then apply this result to the nonlinear wave equation in one dimension. We present the stroboscopic averaging method, which is a numerical method introduced by Chartier, Murua and Sanz-Serna, and apply it to our problem. Finally, we conclude by presenting the qualitative and quantitative efficiency of this numerical method for some nonlinear wave problem.

Dates and versions

hal-01160869 , version 1 (08-06-2015)

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Guillaume Leboucher. Stroboscopic averaging of highly oscillatory nonlinear wave equations. Mathematical Methods in the Applied Sciences, 2015, 38 (9), pp.1746-1766. ⟨10.1002/mma.3183⟩. ⟨hal-01160869⟩
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