Klein-Gordon-Schrdinger方程的辛Fourier拟谱格式(英文)  

Symplectic Fourier Pseudo-spectral Schemes for Klein-Gordon-Schrdinger Equation

作　　者：王兰[1] 马院萍[1] 孔令华[1] 段雅丽[2] 

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 [2]中国科学技术大学数学系,安徽合肥230026

出　　处：《计算物理》2011年第2期275-282,共8页Chinese Journal of Computational Physics

基　　金：NSFC(No.10901074);Natural Science Foundation of Jiangxi Province(No.2008GQS0054);Foundation of Department of Education Jiangxi Province(No.GJJ09147);Young Growth Foundation of Jiangxi Normal University(No.3182);Innovation Foundation in 2010 for Graduate Students(No.YJS2010009);Natural Science Foundation of Anhui Province(No.090416227)

摘　　要：主要讨论Klein-Gordon-Schrdinger方程的Fourier拟谱辛格式,包括中点公式和Strmer/Verlet格式.首先构造一个哈密尔顿方程,针对此哈密尔顿方程,在空间方向用Fourier拟谱离散得到一个有限维的哈密尔顿系统,对此有限维系统在时间方向用Strmer/Verlet方法离散得到KGS方程的完全显式的辛格式.中点格式虽然是隐式的但效率也很高,且具有质量守恒律.数值实验表明,辛格式能够在长时间内很好地模拟各类孤立波.Symplectic Fourier pseudo-spectral integrators for Klein-Gordon-Schrdinger equations（KGS） are investigated.A Hamiltonian formulation is presented.Fourier pseudo-spectral discretization is applied to the space approximation which leads to a finite-dimensional Hamiltonian system.Symplectic integrators,including Strmer/Verlet method and midpoint rule,are adopted in the time direction which leads to symplectic integrators for KGS.It suggests that the Strmer/Verlet method is explicit which can be coded effciently,and the midpoint rule captures mass of the original system exactly.Numerical experiments show that symplectic integrator can simulate various solitary well over a long period.

关 键 词：KGS方程 FOURIER拟谱方法 Stmer/Verlet方法 中点格式 辛积分 

分 类 号：O241.8[理学—计算数学]