### An explicit finite difference scheme for the Camassa-Holm equation

#### 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 the Camassa-Holm equation.

#### Article information

Source
Adv. Differential Equations Volume 13, Number 7-8 (2008), 681-732.

Dates
First available in Project Euclid: 18 December 2012

Mathematical Reviews number (MathSciNet)
MR2479027

Zentralblatt MATH identifier
1191.35021

Subjects
Primary: 65M06: Finite difference methods