A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg-Landau equations
type: Item
instance of: scholarly article
title: A three-level finite difference method with preconditioning technique for two-dimensional nonlinear fractional complex Ginzburg-Landau equations
zbMATH Open document ID: 1462.65119
author: Qifeng Zhang
author: Lu Zhang
author: Hai-Wei Sun
published in: Journal of Computational and Applied Mathematics
publication date: 2021-02-11T00:00:00Z
review text: A three-level linearized finite difference method for the two-dimensional Riesz space-fractional complex nonlinear Ginzburg-Landau equations is studied. The paper is organized as follows. Section 1 is an introduction. In Section 2, some basic and useful lemmas are presented. The numerical scheme and the analysis of the the local truncation error is derived in Section 3. The uniqueness, boundedness, and convergence of the proposed three-level linearized method are given in this section too. In Section 4, a fast preconditioner for solving the resulting discretized complex linear system is proposed. In Section 5, some numerical examples with tables and graphical illustrations are given and analyzed. In Section 6, concluding remarks and some future works are drawn.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65T50
Mathematics Subject Classification ID: 65F08
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 15B05
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35Q56
zbMATH DE Number: 7309613
zbMATH Keywords: space fractional Ginzburg-Landau equation
zbMATH Keywords: Crank-Nicolson scheme
zbMATH Keywords: boundedness
zbMATH Keywords: circulant preconditioner
reviewed by: Temur Jangveladze
MaRDI profile type: Publication
full work available at URL: j.cam.2020.113355
OpenAlex ID: W3116551071
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DOI: 10.1016/J.CAM.2020.113355
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