A self-adaptive moving mesh method for the Camassa-Holm equation |
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Authors: | Bao-Feng Feng Ken-ichi Maruno |
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Institution: | a Department of Mathematics, The University of Texas-Pan American, Edinburg, TX 78539-2999, USA b Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan |
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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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Keywords: | 65M06 35Q58 37K40 |
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