离散空间分数阶非线性薛定谔方程的MHSS型迭代方法

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.

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

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.