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arXiv · 2010.05249

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

Yong-Liang Zhao·Alexander Ostermann·Xian-Ming Gu
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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.

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Yong-Liang Zhao, Alexander Ostermann, Xian-Ming Gu. 2020-10-11. A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations. https://doi.org/10.1016/j.jcp.2021.110652

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