空间分数阶 KGS 方程组的辛差分格式

摘要/Abstract

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.

关键词: 分数阶 KGS 方程组, 守恒格式, 辛格式, 收敛性

Abstract:

In the paper, the symplectic-preserving schemes are presented for fractional Klein-Gordon-Schrödinger 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-Schrödinger 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.

Key words: Fractional Klein-Gordon-Schrödinger equations, Conservative scheme, Symplectic scheme, Convergence

中图分类号:

O242.2

王俊杰. 空间分数阶 KGS 方程组的辛差分格式[J]. 数学物理学报, 2024, 44(5): 1319-1334.

Wang Junjie. Symplectic Difference Scheme for the Space Fractional KGS Equations[J]. Acta mathematica scientia,Series A, 2024, 44(5): 1319-1334.

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