ZK-MEM方程的多辛Preissmann格式  

Multi-Symplectic Preissmann Scheme for ZK-MEM Equation

作　　者：王俊杰[1,2] 王连堂[2] 杨宽德[1] 

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：《杭州师范大学学报（自然科学版）》2012年第5期453-458,共6页Journal of Hangzhou Normal University(Natural Science Edition)

摘　　要：ZK-MEM方程作为一类重要的非线性方程有着许多广泛的应用前景,基于Hamilton空间体系的多辛理论研究了ZK-MEM方程的数值解法,讨论了利用Preissmann方法构造离散多辛格式的途径,并构造了一种典型的半隐式的多辛格式,该格式满足多辛守恒律、局部能量守恒律.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.ZK-MEM equation is a typical nonlinear wave equation with a very wide range of applications. Basing on the multi-symplectic algorithm in Hamilton space systrem, the paper researched on the numerical solutions for ZK-MEM equation, discussed the methods of constructing the discrete multi-symplectic scheme with Preissmann method, and presented a kind of typical semi-implicit multi-symplectic scheme, which satisfied with multi-symplectic conservation laws and partial energy conservation law. The results of numerical experiments show that the discrete multi-symplectic scheme has better long-time numerical stability.

关 键 词：Hamiton系统 PREISSMANN格式 多辛算法 ZK—MEM方程 

分 类 号：O29[理学—应用数学]