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2008 An explicit finite difference scheme for the Camassa-Holm equation
Giuseppe Maria Coclite, Kenneth H. Karlsen, Nils Henrik Risebro
Adv. Differential Equations 13(7-8): 681-732 (2008).

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.

Citation

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Giuseppe Maria Coclite. Kenneth H. Karlsen. Nils Henrik Risebro. "An explicit finite difference scheme for the Camassa-Holm equation." Adv. Differential Equations 13 (7-8) 681 - 732, 2008.

Information

Published: 2008
First available in Project Euclid: 18 December 2012

zbMATH: 1191.35021
MathSciNet: MR2479027

Subjects:
Primary: 65M06
Secondary: 35Q53

Rights: Copyright © 2008 Khayyam Publishing, Inc.

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Vol.13 • No. 7-8 • 2008
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