A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations

Abstract

Fractional Ginzburg-Landau equations as the generalization of the classical one have been used to describe various physical phenomena. In this paper, we propose a numerical integration method for solving space fractional Ginzburg-Landau equations based on a dynamical low-rank approximation. We first approximate the space fractional derivatives by using a fractional centered difference method. Then, the resulting matrix differential equation is split into a stiff linear part and a nonstiff (nonlinear) one. For solving these two subproblems, a dynamical low-rank approach is used. The convergence of our method is proved rigorously. Numerical examples are reported which show that the proposed method is robust and accurate.

17 pages; 3 figures; 4 tables

References in corpus (2)

• Fractional generalization of the Ginzburg-Landau equation: An unconventional approach to critical phenomena in complex media
• Psi-Series Solution of Fractional Ginzburg-Landau Equation

Cited by in corpus (2)

• An adaptive low-rank splitting approach for the extended Fisher--Kolmogorov equation
• Weighted implicit-explicit discontinuous Galerkin methods for two-dimensional Ginzburg-Landau equations on general meshes