A self-adaptive moving mesh method for the Camassa-Holm equation
A self-adaptive moving mesh method for the Camassa-Holm equation
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DOI：
10.1016/j.cam.2010.05.044
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发表时间：
2009-05
期刊：
影响因子：
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通讯作者：
B. Feng;K. Maruno;Y. Ohta
中科院分区：
文献类型：
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作者：
B. Feng;K. Maruno;Y. Ohta
提出了一种自适应移动网格方法，用于Camassa-Holm方程的数值模拟。它是一个可积的方案，因为它具有精确的N-孤子解。由于非均匀网格是由解自动驱动和自适应的，因此称之为自适应移动网格法。一旦非均匀网格被演化，则通过求解三对角线性系统来确定解。由于该方法的这两个上级特性，几个测试问题即使使用少量的网格点也给出了非常令人满意的结果。
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.