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. As- suming 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 the Camassa-Holm equation.
An explicit finite difference scheme for the Camassa-Holm equation
COCLITE, Giuseppe Maria;
2008-01-01
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. As- suming 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 the Camassa-Holm equation.File in questo prodotto:
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