Approximation of the Long-Time Dynamics of the Dynamical System Generated by the Ginzburg-Landau Equation
Year: 2023
Author: Cristina Tone, Florentina Tone
Communications in Mathematical Research , Vol. 39 (2023), Iss. 4 : pp. 501–522
Abstract
In this article we consider the (complex) Ginzburg-Landau equation, we discretize in time using the implicit Euler scheme, and with the aid of the discrete Gronwall lemma and of the discrete uniform Gronwall lemma we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2023-0003
Communications in Mathematical Research , Vol. 39 (2023), Iss. 4 : pp. 501–522
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Ginzburg-Landau equation implicit Euler scheme long-time stability attractors.