Preprint 2008-006
An explicit finite difference scheme for the Camassa–Holm equation
Giuseppe Maria Coclite, Kenneth H. Karlsen and Nils Henrik Risebro
Abstract: We put forward and analyze an explicit finite difference scheme for the Camassa–Holm shallow water equation that can handle general H1 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 H1 towards a dissipative weak solution of Camassa–Holm equation.