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

作　　者：王俊杰[1] 李胜平[1] WANG Junjie LI Shengping(Mathematics and Statistics Institute of Pu＇er University, Pu＇er 665000, Yunnan, China.)

机构地区：[1]普洱学院数学与统计学院,云南普洱665000

出　　处：《数学年刊（A辑）》2016年第3期291-302,共12页Chinese Annals of Mathematics

基　　金：云南省教育厅基金(No.2015y490);普洱学院创新团队(No.CXTD003)的资助

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.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.

关 键 词：HAMILTON系统 普雷斯曼格式 多辛算法 强色散DGH方程 

分 类 号：O241.82[理学—计算数学]