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arXiv:0802.3129 [math.AP]AbstractReferencesReviewsResources

An explicit finite difference scheme for the Camassa-Holm equation

Giuseppe Maria Coclite, Kenneth H. Karlsen, Nils Henrik Risebro

Published 2008-02-21Version 1

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 strongly in $H^1$ towards a dissipative weak solution of Camassa-Holm equation.

Comments: 45 pages, 6 figures
Categories: math.AP, math.NA
Subjects: 35G25, 35L05, 65M06, 65M12
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