Camassa-Holm方程的多辛Fourier拟谱格式  

Multi-Symplectic Fourier Pseudo-Spectral Scheme of the Camassa-Holm Equation

作　　者：陈亚铭[1] 宋松和[1,2] 

机构地区：[1]国防科技大学数学与系统科学系,湖南长沙410073 [2]南洋理工大学物理与数学科学学院数学系

出　　处：《湘潭大学自然科学学报》2009年第3期13-17,共5页Natural Science Journal of Xiangtan University

基　　金：国家自然科学基金资助项目(10571178)

摘　　要：对满足周期边界条件的Camassa-Holm(CH)方程,基于其多辛方程组的形式,空间方向用Fourier拟谱方法,时间方向用中点隐式辛格式进行离散,得到了CH方程的多辛Fourier拟谱格式及其离散的多辛守恒律.数值实验验证了所构造格式的有效性与长期数值稳定性.The Camassa-Holm equation（CHE） with periodic boundary condition is considered in this paper. Based on its multi-symplectic formulation, a multi-symplectic Fourier pseudo-spectral scheme for the CHE is constructed by using Fourier pseudo-spectral method in space direction and midpoint implicit symplectic scheme in time direction. Its discrete multi-symplectic conservation law is also obtained. Numerical experiments show that the scheme constructed in this paper is effective and has excellent long time numerical behavior.

关 键 词：Camassa—Holm方程 FOURIER拟谱格式 多辛 

分 类 号：O241.82[理学—计算数学]