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arXiv · 0905.2693

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

Bao-Feng Feng·Ken-ichi Maruno·Yasuhiro Ohta
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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.

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Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta. 2010-04-26. A self-adaptive mesh method for the Camassa-Holm equation. https://arxiv.org/abs/0905.2693

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