Antoine, X., Lorin, E. and Zhang, Y. (2021) Derivation and Analysis of Computational Methods for Fractional Laplacian Equations with Absorbing Layers. Numerical Algorithms, 87, 409-444.
https://doi.org/10.1016/j.jcp.2019.04.025

has been cited by the following article:

• TITLE: Stability of Perfectly Matched Layers for Time Fractional Schrödinger Equation

  AUTHORS: Tingting Zhang, Xiangkun Li

  KEYWORDS: Time Fractional Schrödinger Equation, Perfectly Matched Layer, Stability

  JOURNAL NAME: Engineering, Vol.15 No.1, January 30, 2023

  ABSTRACT: It is an important issue to numerically solve the time fractional Schrödinger equation on unbounded domains, which models the dynamics of optical solitons propagating via optical fibers. The perfectly matched layer approach is applied to truncate the unbounded physical domain, and obtain an initial boundary value problem on a bounded computational domain, which can be efficiently solved by the finite difference method. The stability of the reduced initial boundary value problem is rigorously analyzed. Some numerical results are presented to illustrate the accuracy and feasibility of the perfectly matched layer approach. According to these examples, the absorption parameters and the width of the absorption layer will affect the absorption effect. The larger the absorption width, the better the absorption effect. There is an optimal absorption parameter, the absorption effect is the best.