A Jacobi Collocation Method for the Fractional Ginzburg-Landau Differential Equation

Authors

  • Yin Yang Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
  • Jianyong Tao Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, School of Mathematics
  • Shangyou Zhang Department of Mathematics Science, University of Delaware, Newark 19716, USA
  • Petr V. Sivtsev International Scientific and Research Laboratory of Multiscale Model Reduction and High Performance Computing, Ammosov North Eastern University, Kulakovskogo, 677013, Yakutsk, Russia

DOI:

https://doi.org/10.4208/aamm.OA-2019-0070

Keywords:

The fractional Ginzburg-Landau equation, Jacobi collocation method, convergence.

Abstract

In this paper, we design a collocation method to solve the fractional Ginzburg-Landau equation. A Jacobi collocation method is developed and implemented in two steps. First, we space-discretize the equation by the Jacobi-Gauss-Lobatto collocation (JGLC) method in one- and two-dimensional space. The equation is then converted to a system of ordinary differential equations (ODEs) with the time variable based on JGLC. The second step applies the Jacobi-Gauss-Radau collocation (JGRC) method for the time discretization. Finally, we give a theoretical proof of convergence of this Jacobi collocation method and some numerical results showing the proposed scheme is an effective and high-precision algorithm.

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Published

2020-03-06

Issue

Vol. 12 No. 1 (2020)

Section

Articles