Klein-Gordon-Schrödinger方程的辛Fourier拟谱格式

计算物理 ›› 2011, Vol. 28 ›› Issue (2): 275-282.

Klein-Gordon-Schrödinger方程的辛Fourier拟谱格式

王兰¹, 马院萍¹, 孔令华¹, 段雅丽²

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

收稿日期:2009-12-28 修回日期:2010-09-01 出版日期:2011-03-25 发布日期:2011-03-25
作者简介:王兰(1979-),female,Chizhou,Anhui,major in numerical solution of PDEs.
基金资助:
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)

Symplectic Fourier Pseudo-spectral Schemes for Klein-Gordon-Schrödinger Equation

WANG Lan¹, MA Yuanping¹, KONG Linghua¹, DUAN Yali²

1. School of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China;
2. School of Mathematical Science, University of Science and Technology of China, Hefei 230026, China

Received:2009-12-28 Revised:2010-09-01 Online:2011-03-25 Published:2011-03-25

摘要/Abstract

摘要： 主要讨论Klein-Gordon-Schrödinger方程的Fourier拟谱辛格式,包括中点公式和Störmer/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Störmer/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.

关键词: KGS方程, Fourier拟谱方法, Stö, mer/Verlet方法, 中点格式, 辛积分

Abstract: Symplectic Fourier pseudo-spectral integrators for Klein-Gordon-Schrödinger 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 Störmer/Verlet method and midpoint rule,are adopted in the time direction which leads to symplectic integrators for KGS.It suggests that the Störmer/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.

Key words: KGS equation, Fourier pseudo-spectral method, Störmer/Verlet method, midpoint rule, symplectic integrator

中图分类号:

O241.8

王兰, 马院萍, 孔令华, 段雅丽. Klein-Gordon-Schrödinger方程的辛Fourier拟谱格式[J]. 计算物理, 2011, 28(2): 275-282.

WANG Lan, MA Yuanping, KONG Linghua, DUAN Yali. Symplectic Fourier Pseudo-spectral Schemes for Klein-Gordon-Schrödinger Equation[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 28(2): 275-282.