空间分数阶Schrödinger方程的PMHSS迭代方法  

PMHSS iterative method for the space-fractional Schrödinger equations

作　　者：熊子慷 尹斯乐 兰冰艳 凌永辉 XIONG Zikang;YIN Sile;LAN Bingyan;LING Yonghui(School of mathematics and statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China;Fujian Key Laboratory of Granular Computing and Applications,Zhangzhou,Fujian 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]福建省粒计算及其应用重点实验室,福建漳州363000

出　　处：《闽南师范大学学报(自然科学版)》2025年第1期100-107,共8页Journal of Minnan Normal University:Natural Science

基　　金：福建省自然科学基金(2022J01896)。

摘　　要：考虑一类空间分数阶Schrödinger方程离散化得到的复线性方程组的快速求解算法,该线性方程组的系数矩阵为稠密的Toeplitz矩阵与三对角矩阵的和。采用了预条件修正Hermite矩阵和反Hermite矩阵分裂(PMHSS)迭代法进行求解,这种方法能够将其转为求解四个对称正定实线性方程组而避免了复值运算,并证明了该迭代法的无条件收敛性。数值结果验证了该方法的有效性。The main focus of this paper is on the fast solution algorithms for the complex linear system obtained by discretizing a class of space-fractional Schrödinger equations.The coefficient matrix of this linear system is the sum of a dense Toeplitz matrix and a tridiagonal matrix.The preconditioned modified Hermite matrix and skew-Hermite matrix splitting(PMHSS)iterative method is used to solve it.This method can be converted into solving four symmetric positive definite real linear systems and avoid complex-valued operations.The unconditional convergence of the iterative method is proved.The numerical results show the effectiveness of this method.

关 键 词：空间分数阶Schrödinger方程 PMHSS迭代法 TOEPLITZ矩阵 

分 类 号：O175[理学—数学]