空间分数阶KGS方程组的辛差分格式  

Symplectic Difference Scheme for the Space Fractional KGS Equations

作　　者：王俊杰 Wang Junjie(School of Mathematics and Statistics,Pu'er University,Yunnan Pu'er 665000)

机构地区：[1]普洱学院数学与统计学院,云南普洱665000

出　　处：《数学物理学报（A辑）》2024年第5期1319-1334,共16页Acta Mathematica Scientia

基　　金：国家自然科学基金(12161070)。

摘　　要：该文研究分数阶KGS方程组的辛差分格式.首先,作者给出了无穷维分数阶Hamilton系统,并将KGS方程组转化为Hamilton系统.然后,基于分数阶中心差分格式对分数阶KGS方程组进行空间离散,得到的半离散系统是一个有限维Hamilton系统.接着,利用辛中点格式对时间进行离散得到全离散格式,并且对该格式进行了守恒性分析.最后,通过数值实验验证了该数值格式的有效性.In the paper,the symplectic-preserving schemes are presented for fractional Klein-Gordon-Schrodinger equations.First,we give the infinite-dimensional Hamilton with fractional Laplacian operator and conservation laws,and change the above quantum mechanical equations into Hamilton system.We apply the central finite difference schemes to discrete Klein-Gordon-Schrodinger in space,and yield a large Hamilton ordinary differential system.Second,we use the midpoint rule in time to Hamiltonian ordinary differential system,and obtain a symplectic approximation of the these equations.Moreover,we analyze the conservation of the numerical scheme.Finally,we give numerical experiments to show the verify the efficiency of the conservative finite difference scheme.

关 键 词：分数阶KGS方程组 守恒格式 辛格式 收敛性 

分 类 号：O242.2[理学—计算数学]