A self-adaptive moving mesh method for the Camassa-Holm equation

Authors:
Bao-Feng Feng;Ken-ichi Maruno;Yasuhiro Ohta
Affiliations:
Department of Mathematics, The University of Texas-Pan American, Edinburg, TX 78539-2999, USA;Department of Mathematics, The University of Texas-Pan American, Edinburg, TX 78539-2999, USA;Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

A self-adaptive moving mesh method is proposed for the numerical simulations of the Camassa-Holm equation. It is an integrable scheme in the sense that it possesses the exact N-soliton solution. It is named a self-adaptive moving mesh method, because the non-uniform mesh is driven and adapted automatically by the solution. Once the non-uniform mesh is evolved, the solution is determined by solving a tridiagonal linear system. Due to these two superior features of the method, several test problems give very satisfactory results even if by using a small number of grid points.