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离散空间分数阶非线性薛定谔方程的MHSS型迭代方法

朱禹, 陈芳   

  1. 北京信息科技大学理学院, 北京 100192
  • 收稿日期:2020-12-31 出版日期:2022-07-14 发布日期:2022-08-03
  • 通讯作者: 陈芳,Email:chenfreesky@126.com.
  • 基金资助:
    北京市教育委员会科学研究计划项目(KM201911232010)资助.

朱禹, 陈芳. 离散空间分数阶非线性薛定谔方程的MHSS型迭代方法[J]. 计算数学, 2022, 44(3): 368-378.

Zhu Yu, Chen Fang. ON MHSS-TYPE ITERATION METHOD FOR DISCRETE SPACE FRACTIONAL NONLINEAR SCHRODINGER EQUATIONS[J]. Mathematica Numerica Sinica, 2022, 44(3): 368-378.

ON MHSS-TYPE ITERATION METHOD FOR DISCRETE SPACE FRACTIONAL NONLINEAR SCHRODINGER EQUATIONS

Zhu Yu, Chen Fang   

  1. School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China
  • Received:2020-12-31 Online:2022-07-14 Published:2022-08-03
利用隐式守恒型差分格式来离散空间分数阶非线性薛定谔方程,可得到一个离散线性方程组.该离散线性方程组的系数矩阵为一个纯虚数复标量矩阵、一个对角矩阵与一个对称Toeplitz矩阵之和.基于此,本文提出了用一种\textit{修正的埃尔米特和反埃尔米特分裂}(MHSS)型迭代方法来求解此离散线性方程组.理论分析表明,MHSS型迭代方法是无条件收敛的.数值实验也说明了该方法是可行且有效的.
By using the implicit conservative difference scheme to discretize the space fractional nonlinear Schrödinger equation, we obtain a discrete linear system, whose coefficient matrix is the sum of a purely complex scalar matrix, a diagonal matrix and a symmetric Toeplitz matrix. Based on this property, we propose a modified Hermitian and skew-Hermitian splitting (MHSS-type) iteration method to solve the discrete linear system. Theoretical analyses show that the MHSS-type iteration method is unconditionally convergent, and numerical experiments show that this method is also feasible and effective.

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