On HSS-like iteration method for the space fractional coupled nonlinear Schrödinger equations
On HSS-like iteration method for the space fractional coupled nonlinear Schrödinger equations
复制标题
DOI：
10.1016/j.amc.2015.09.028
复制
发表时间：
2015-11
期刊：
影响因子：
--
通讯作者：
Yu-Hong Ran;Jungang Wang;Dongling Wang
中科院分区：
文献类型：
--
作者：
Yu-Hong Ran;Jungang Wang;Dongling Wang
采用无条件稳定的分数阶中心差分格式的隐式守恒差分格式离散空间分数阶耦合非线性薛定谔方程。离散化线性系统的系数矩阵等于一个复尺度单位矩阵和一个对称的对角加Toeplitz矩阵之和，复尺度单位矩阵可以写成虚单位乘以单位矩阵。本文提出了一种求解离散线性方程组的类HSS迭代方法。理论分析表明，类HSS迭代法是无条件收敛的。数值例子说明了HSS类迭代方法的有效性。
The implicit conservative difference scheme with the fractional centered difference formula, which is unconditionally stable, is employed to discretize the space fractional coupled nonlinear Schrödinger equations. The coefficient matrix of the discretized linear system is equal to the sum of a complex scaled identity matrix which can be written as the imaginary unit times the identity matrix and a symmetric diagonal-plus-Toeplitz matrix. In this paper, the HSS-like iteration method is proposed to solve the discretized linear system. Theoretical analyses show that the HSS-like iteration method is unconditionally convergent. Numerical examples are presented to illustrate the effectiveness of the HSS-like iteration method.