Fast iteration method for nonlinear fractional complex Ginzburg-Landau equations

In this paper, we solve the nonlinear space fractional complex Ginzburg-Landau equations. The motivation of this work is to give a fast numerical method to solve the linear system, which is obtained from the nonlinear space fractional complex Ginzburg-Landau equations. The coefficient matrix of the linear system is the sum of a complex diagonal matrix and a real Toeplitz matrix. The significance of this work is that the new method has a superiority in computation because we can use the circulant preconditioner and the fast Fourier transform to solve the linear system. Numerical examples are tested to illustrate the advantage of the numerical method.

Automated summary

The paper presents a fast numerical method for solving the nonlinear space fractional complex Ginzburg-Landau equations, utilizing a circulant preconditioner and fast Fourier transform to solve the linear system, resulting in computational superiority. Numerical examples are conducted to demonstrate the advantage of the method.