Dirac方程的多辛格式  

Multi-symplectic Method for the Dirac Equation

作　　者：王健[1] 

机构地区：[1]上海交通大学数学系,上海200240

出　　处：《上海交通大学学报》2004年第5期849-852,共4页Journal of Shanghai Jiaotong University

摘　　要：基于Bridges原理,得到了1+1维Dirac方程的多辛哈密尔顿系统形式及局部守恒律.空间方向采用Fourier拟谱格式,时间方向为中点辛格式,得到的多辛半离散和全离散格式满足局部多辛守恒.证明了波函数模方和局部能量守恒.数值结果表明了算法的长时间有效性.Based on Bridges's principle, the multi-symplectic form of 1+1 dimension Dirac equation and local conservation laws were obtained. The Fourier pseudospectral discretization in space and the midpoint symplectic discretization in time are considered. Both the multi-symplectic semi-discretization and full-discretization satisfy the local conservation laws. The conservation of the modul of wavefunction and local energy was proved. Numerical results were also reported to show the long time effectiveness of the schemes.

关 键 词：多辛格式 局部守恒律 FOURIER拟谱格式 DIRAC方程 

分 类 号：O241.82[理学—计算数学]