非线性四阶Schrdinger方程的分裂多辛拟谱格式  

SPLIT-STEP MULTI-SYMPLECTIC PSEUDO-SPECTRAL SCHEME FOR THE NONLINEAR FOURTH-ORDER SCHRDINGER EQUATION

作　　者：黄浪扬[1] 

机构地区：[1]华侨大学数学科学学院,泉州362021

出　　处：《高等学校计算数学学报》2014年第2期183-192,共10页Numerical Mathematics A Journal of Chinese Universities

基　　金：福建省自然科学基金资助项目(2011J01010);中央高校基本科研业务费专项资金资助;华侨华侨大学侨办科研基金资助项目(10QZR21);国家自然科学基金资助项目(11271171,10901074,11126330)

摘　　要：自冯康院士首次由辛几何的观点提出计算Hamilton系统的辛几何算法^([1-2])后,Bridges和Reich又引入了一个基于某个守恒型偏微分方程多辛结构的多辛积分的概念^([3-4]).对物理学中具有广泛应用的广义高阶非线性Schr(o|")A Multi-symplectic Fourier pseudo-spectral scheme for the fourth- order Schrodinger equation with cubic nonlinear term is constructed. We prove that the scheme satisfies full-discrete multi-symplectic conservation laws and charge conservation laws. Then, a split-step multi-symplectic pseudo-spectral scheme is proposed by using the time splitting method. Numerical experiments show that the two schemes constructed in this paper are effective and practicable, and the split-step multi-symplectic pseudo-spectral scheme is significantly better than the multi-symplectic Fourier pseudo-spectral scheme in preserving the charge conservation laws of the original equation and consuming CPU time

关 键 词：非线性SCHRODINGER方程 分裂算法 拟谱格式 HAMILTON系统 辛几何算法 四阶 偏微分方程 多辛积分 

分 类 号：O241.82[理学—计算数学]