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; Karlsen, K. H.; Risebro, N. H.. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - 13:7-8(2008), pp. 681-732.
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
