一类高阶KdV类型水波方程的多辛Preissmann格式  

Multi-symplectic Preissmann scheme for a high order wave equation of KdV type

作　　者：李胜平[1] 王俊杰[1,2] 

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

出　　处：《西北师范大学学报（自然科学版）》2017年第1期36-44,52,共10页Journal of Northwest Normal University(Natural Science)

基　　金：云南省教育厅项目(2015Y490);普洱学院创新团队资助项目(CXTD003)

摘　　要：高阶KdV类型水波方程作为一类重要的非线性方程有着广泛的应用前景.基于Hamilton空间系的多辛理论研究了一类高阶KdV类型水波方程的数值解法,利用Preissmann方法构造了离散半隐式的多辛格式,该格式满足多辛守恒律.数值算例表明该多辛离散格式具有较好的长时间数值稳定性.A high order wave equation of KdV type, a typical nonlinear wave equation, is sdudied based on the multi-sympleetic theory in Hamilton space. The multi-symplectic formulations of a high order wave equation of KdV type with several conservation laws are presented. The symplectic Preissmann method is used to discretize the formulations. The numerical experiment of the solitary wave is given, and the results verify the efficiency of the multi-symplectic scheme.

关 键 词：Hamiton系统 PREISSMANN格式 多辛算法 高阶KdV类型水波方程 

分 类 号：O241.82[理学—计算数学]