一类DGH方程的新保结构算法研究  

Research on new structure-preserving algorithms for a DGH equation

作　　者：王俊杰[1,2] 

机构地区：[1]普洱学院数学系,云南普洱665000 [2]西北大学数学学院,陕西西安710127

出　　处：《大连理工大学学报》2016年第4期432-440,共9页Journal of Dalian University of Technology

基　　金：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)

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.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.

关 键 词：哈密顿系统 保结构算法 多辛理论 DGH方程 

分 类 号：O29[理学—应用数学]