A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations
arXiv:2010.05249 · doi:10.1016/j.jcp.2021.110652
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.
arXiv comment17 pages; 3 figures; 4 tables
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