Method of lines study of nonlinear dispersive waves
| Autor: | William E. Schiesser, Philippe Saucez, A. Vande Wouwer, Paul Andries Zegeling |
|---|---|
| Rok vydání: | 2004 |
| Předmět: |
Finite differences
Partial differential equation Kaup–Kupershmidt equation Applied Mathematics Method of lines Mathematical analysis First-order partial differential equation Wave equation Kadomtsev–Petviashvili equation Adaptive mesh refinement Dispersionless equation Computational Mathematics Nonlinear Sciences::Exactly Solvable and Integrable Systems N-soliton solution Korteweg-de Vries equation Korteweg–de Vries equation Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 168(1-2):413-423 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2003.12.012 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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