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arXiv · 0802.3129

An explicit finite difference scheme for the Camassa-Holm equation

Giuseppe Maria Coclite·Kenneth H. Karlsen·Nils Henrik Risebro
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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 strongly in $H^1$ towards a dissipative weak solution of Camassa-Holm equation.

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Giuseppe Maria Coclite, Kenneth H. Karlsen, Nils Henrik Risebro. 2008-02-21. An explicit finite difference scheme for the Camassa-Holm equation. https://arxiv.org/abs/0802.3129

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