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.
- Integrable semi-discretization
- Peakon and cupson solutions
- Self-adaptive moving mesh method
- The Camassa-Holm equation
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics