多辛Preissman格式及其应用  

Multisymplectic Preissman Scheme and Its Application

作　　者：王兰[1] 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《江西师范大学学报（自然科学版）》2009年第1期42-46,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：江西省自然科学基金(2008GQS0054);江西省教育厅科技基金(GJJ0914Z);江西师范大学青年成长基金(2390)资助项目

摘　　要：主要讨论了用于求解多辛哈密尔顿系统的多辛Preissman格式及其简单应用.根据多辛格式必须满足离散的多辛守恒律的基本思想,从Runge-Kutta方法入手,推导出其为多辛格式的充分条件,进而得到了多辛的中点格式,同时举例说明的它在偏微分方程数值求解中的应用.We discuss the muhisymplectic Preissman scheme which is mainly applied to solve muhisymplectic Hamiltonian system in the paper. The simple application of the numerical method is also studied. The basic idea to construct multi- symplectic scheme is that it must satisfy discrete mnltisymplectic conservation law. Based on the idea, we derive the sufficient conditions that lead a pair of Runge-Kutta methods to muhisymplectic. Therefore, the muhisymplectic Preissman scheme is obtained. We take wave equation as an example to illustrate the application of mnltisymplectic Preissman scheme in the numerically solving partial differential equations.

关 键 词：哈密尔顿系统 多辛格式 Preissman格式 波动方程 

分 类 号：O241.8[理学—计算数学]