论文标题
非线性分数复合物Ginzburg-Landau方程
A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations
论文作者
论文摘要
作为经典的概括，Ginzburg-Landau方程已被用来描述各种物理现象。在本文中，我们提出了一种基于动力学低级别近似的数值集成方法，用于求解空间分数Ginzburg-Landau方程。我们首先使用分数中心差方法近似空间分数衍生物。然后，所得的矩阵微分方程分为刚性线性部分和一个非势头（非线性）。为了解决这两个子问题，使用了动态的低级方法。我们方法的融合被严格证明。报道了数值示例，表明所提出的方法是鲁棒且准确的。
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.
