AuthorsG. M. Coclite, K. H. Karlsen and N. H. Risebro
TitleAn Explicit Finite Difference Scheme for the Camassa-Holm Equation
AfilliationCenter for Biomedical Computing (SFF), Scientific Computing
Project(s)Center for Biomedical Computing (SFF)
StatusPublished
Publication TypeJournal Article
Year of Publication2008
JournalAdvances in Differential Equations
Volume13
Number7-8
Pagination681-732
Abstract

We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general H 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 stongly in H 1 towards a dissipative weak solution of Camassa-Holm equation.

Citation KeySimula.sc.928