Year: 2020
Author: Yin Yang, Jianyong Tao, Shangyou Zhang, Petr V. Sivtsev
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 57–86
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0070
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 1 : pp. 57–86
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: The fractional Ginzburg-Landau equation Jacobi collocation method convergence.
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