A Note on Stability of Parabolic Difference Equations on Torus. (26th April 2023)

• Record Type: Journal Article
• Authors: Ashyralyev, Allaberen; Hezenci, Fatih; Sozen, Yasar
• Is Part Of: Numerical functional analysis and optimization. Volume 44:Number 6(2023)
• Page Start: 490
• Page End: 509
• Publication Date: 2023-04-26
• Subjects: Difference equations on manifolds -- difference schemes -- self-adjoint positive definite operator -- well-posedness; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2023.2183509
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The present article investigates nonlocal boundary value problems for parabolic equations of reverse type on torus. The first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle T 1 and torus T 2 are presented. For the solutions of the difference scheme, the stability estimates and coercivity estimates in various Hölder norms are established. Furthermore, theoretical results are supported by numerical experiments.