| 王俊杰,李胜平.一类强色散DGH方程的多辛普雷斯曼格式[J].数学年刊A辑,2016,37(3):291~302 |
| 一类强色散DGH方程的多辛普雷斯曼格式 |
| Multi-symplectic Preissmann Methods for DGH Equation with Strong Dispersive Term |
| Revised:June 25, 2015 |
| DOI： |
| 中文关键词: Hamilton 系统, 普雷斯曼格式, 多辛算法, 强色散DGH 方程 |
| 英文关键词:Hamilton system, Preissmann scheme,
Multi-symplectic method, The DGH equation with strong dispersive term |
| 基金项目:本文受到云南省教育厅基金(No.2015y490)和普洱学院创新团队(No.CXTD003)的资助. |
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| 中文摘要: |
| DGH 方程作为一类重要的非线性水波方程有着许多广泛的应用前景. 基于Hamilton
系统的多辛理论研究了一类强色散DGH 方程的数值解法, 利用多辛普雷斯曼
方法构造了一种典型的半隐式的多辛格式. 分析了该格式的局部能量和动量守恒律误差, 并给出了数值算例.
数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性. |
| 英文摘要: |
| The DGH equation, a typical nonlinear wave
equation, has broad application prospect. The numerical method of
the DGH equation with a strong dispersive term was studied based on
the multi-symplectic theory in the Hamilton space. The
multi-symplectic Preissmann is reviewed, and semi-implicit scheme is
constructed to solve the DGH equation with a strong dispersive term,
and the error of local conservation laws of energy and momentum are
given. The numerical experiments are given, and results show that
the numerical method is an efficient method with excellent long-time
numerical behaviors. |
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