空间分数阶Ginzburg-Landau方程的快速求解

Fast solution of spatial fractional Ginzburg-Landau equation

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.