Stroboscopic averaging of highly oscillatory nonlinear wave equations |
| |
| Authors: | G. Leboucher |
| |
| Affiliation: | INRIA‐Rennes, IRMAR, 35042 Rennes Cedex, France |
| |
| 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. |
| |
| Keywords: | highly oscillatory evolution equation stroboscopic averaging nonlinear wave equation |
|
|
