Method of lines study of nonlinear dispersive waves
- 作者：Saucez ; P. ; Vande Wouwer ; A. ; Schiesser ; W.E. ; Zegeling ; P.
- 关键词：Method of lines ; Adaptive mesh refinement ; Finite differences ; N-soliton solution ; Korteweg-de Vries equation ; Kaup&ndash ; Kupershmidt equation
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：2004
- 期刊代码：72_03770427
- 类别：cp
- 出版时间：July 1, 2004
- 卷：168
- 期：1-2
- 页码：413-423
- 文件大小：541 K
摘要
In this study, we consider partial differential equation problems describing nonlinear wave phenomena, e.g., a fully nonlinear third order Korteweg-de Vries (KdV) equation, the fourth order Boussinesq equation, the fifth order Kaup–Kupershmidt equation and an extended KdV5 equation. First, we develop a method of lines solution strategy, using an adaptive mesh refinement algorithm based on the equidistribution principle and spatial regularization techniques. On the resulting highly nonuniform spatial grids, the computation of high-order derivative terms appears particularly delicate and we focus attention on the selection of appropriate approximation techniques. Finally, we solve several illustrative problems and compare our computational approach to conventional solution techniques.