English

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 H1H^1 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 H1H^1 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

R2 v1 2026-06-21T10:14:42.871Z