An explicit finite difference scheme for the Camassa-Holm equation
Analysis of PDEs
2008-02-22 v1 Numerical Analysis
Abstract
We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general initial data and thus peakon-antipeakon interactions. Assuming a specified condition restricting the time step in terms of the spatial discretization parameter, we prove that the difference scheme converges strongly in towards a dissipative weak solution of Camassa-Holm equation.
Cite
@article{arxiv.0802.3129,
title = {An explicit finite difference scheme for the Camassa-Holm equation},
author = {Giuseppe Maria Coclite and Kenneth H. Karlsen and Nils Henrik Risebro},
journal= {arXiv preprint arXiv:0802.3129},
year = {2008}
}
Comments
45 pages, 6 figures