摘要
主要讨论Klein-Gordon-Schrdinger方程的Fourier拟谱辛格式,包括中点公式和Strmer/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Strmer/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-Schrdinger 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 Strmer/Verlet method and midpoint rule,are adopted in the time direction which leads to symplectic integrators for KGS.It suggests that the Strmer/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.
出处
《计算物理》
CSCD
北大核心
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)
