The Study of the Numerical Treatment of the Real Ginzburg–Landau Equation Using the Galerkin Method. (27th July 2021)

• Record Type: Journal Article
• Authors: Chin, Pius W. M.
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 10(2021)
• Page Start: 1154
• Page End: 1177
• Publication Date: 2021-07-27
• Subjects: Real Ginzburg–Landau equation -- nonlinear equation -- nonstandard finite difference method -- Galerkin method -- optimal rate of convergence; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1948863
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The real Ginzburg–Landau equation is studied in this article. We proceed and use the Galerkin method in combination with the compactness theorem to show that the solution of this problem exists and is unique in appropriate Sobolev spaces. This is proceeded by the designing of a reliable nonlinear numerical scheme from the afore mentioned problem and further show that this scheme is stable. Furthermore, the optimal rate of convergence of the scheme is determined in some appropriate spaces with emphasizes on the fact that the numerical solution from this scheme preserves all the qualitative properties of the exact solution and the numerical experiments are conducted with the help of an example to justify the theory.