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

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

2009-05-16

arxiv.org/abs/0905.2693v3

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

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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