空间分数阶Ginzburg-Landau方程的快速求解  

Fast solution of spatial fractional Ginzburg-Landau equation

作　　者：宋岩 王小利 凌永辉 SONG Yan;WANG Xiaoli;LING Yonghui(School of Mathematics and Statistics,Minnan Normal University,363000,Zhangzhou,Fujian,PRC)

机构地区：[1]闽南师范大学数学与统计学院,福建省漳州市363000

出　　处：《曲阜师范大学学报（自然科学版）》2023年第1期32-40,共9页Journal of Qufu Normal University(Natural Science)

基　　金：福建省自然科学基金(2016J05015).

摘　　要：对于空间分数阶Ginzburg-Landau方程在离散过程中产生的带有Toeplitz矩阵的线性系统,给出了一种新的快速求解方法.该方法基于循环矩阵可替代Toeplitz矩阵,转变为求解带有预处理的线性系统,因而具有计算优势,并分析了该方法的系数矩阵特征值分布.数值试验表明,该方法比PGSOR法具有更好的收敛行为.For the linear system with Toeplitz matrix generated in the discrete process of spatial fractional Ginzburg-Landau equation,a new fast solution method is presented.The method is based on the substitution of Toeplitz matrix by cyclic matrix,which is transformed into solving linear system with preprocessing.The eigenvalue distribution of the coefficient matrix is analyzed.Numerical experiments show that this method has better convergence behavior than PGSOR method.

关 键 词：分数阶Ginzburg-Landau方程 预处理 循环矩阵 特征值 

分 类 号：O241.7[理学—计算数学]