Taiwanese Journal of Mathematics

The Spectral Method for Long-time Behavior of a Fractional Power Dissipative System

Hong Lu and Mingji Zhang

Full-text: Open access

Abstract

In this paper, we consider the fractional complex Ginzburg-Landau equation in two spatial dimensions with the dissipative effect given by a fractional Laplacian. The periodic initial value problem of the fractional complex Ginzburg-Landau equation is discretized fully by Galerkin-Fourier spectral method, and the dynamical behaviors of the discrete system are studied. The existence and convergence of global attractors of the discrete system are obtained by a priori estimates and error estimates of the discrete solution. The numerical stability and convergence of the discrete scheme are proved.

Article information

Source
Taiwanese J. Math., Volume 22, Number 2 (2018), 453-483.

Dates
Received: 26 October 2016
Revised: 24 August 2017
Accepted: 12 September 2017
First available in Project Euclid: 14 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1507946430

Digital Object Identifier
doi:10.11650/tjm/170902

Mathematical Reviews number (MathSciNet)
MR3780728

Zentralblatt MATH identifier
06965381

Subjects
Primary: 65M12: Stability and convergence of numerical methods 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65N35: Spectral, collocation and related methods

Keywords
fractional Ginzburg-Landau equation global attractor numerical stability spectral method

Citation

Lu, Hong; Zhang, Mingji. The Spectral Method for Long-time Behavior of a Fractional Power Dissipative System. Taiwanese J. Math. 22 (2018), no. 2, 453--483. doi:10.11650/tjm/170902. https://projecteuclid.org/euclid.twjm/1507946430


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