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- Title
Stroboscopic averaging of highly oscillatory nonlinear wave equations.
- Authors
Leboucher, G.
- 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. Copyright © 2014 John Wiley & Sons, Ltd.
- Subjects
NONLINEAR wave equations; AVERAGING method (Differential equations); BANACH spaces; EVOLUTION equations; NUMERICAL analysis
- Publication
Mathematical Methods in the Applied Sciences, 2015, Vol 38, Issue 9, p1746
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.3183