| 王俊杰.一类DGH方程的新保结构算法研究[J].,2016,56(4):432-440 |
| 一类DGH方程的新保结构算法研究 |
| Research on new structure-preserving algorithms for a DGH equation |
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| DOI：10.7511/dllgxb201604016 |
| 中文关键词: 哈密顿系统 保结构算法 多辛理论 DGH方程 |
| 英文关键词: Hamilton system structure-preserving algorithms multi-symplectic theory DGH equation |
| 基金项目:云南省教育厅科学研究基金资助项目(2015y490)；普洱学院创新团队项目(CXTD003). |
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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广泛的应用前景．基于哈密顿系统的多辛理论研究了一类DGH方程的数值解法，利用平均向量场方法对此哈密顿系统进行了数值离散，构造了DGH方程的局部能量保结构算法和局部动量保结构算法．数值算例表明，这两种保结构算法具有较好的长时间数值稳定性． |
| 英文摘要: |
| DGH equation is an important nonlinear wave equation and has broad application prospect. Numerical method for the equation is studied based on the multi-symplectic theory in Hamilton system. The average vector field (AVF) method is used to discretize the Hamilton system, and local energy structure-preserving algorithm and local momentum structure-preserving algorithm are constructed to solve the DGH equation. The numerical examples show that the two kinds of structure-preserving algorithms have good long-time numerical stability. |
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