Advances in Differential Equations

An explicit finite difference scheme for the Camassa-Holm equation

Giuseppe Maria Coclite, Kenneth H. Karlsen, and Nils Henrik Risebro

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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

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

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 65M06: Finite difference methods
Secondary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]


Coclite, Giuseppe Maria; Karlsen, Kenneth H.; Risebro, Nils Henrik. An explicit finite difference scheme for the Camassa-Holm equation. Adv. Differential Equations 13 (2008), no. 7-8, 681--732.

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