Electron. J. Differential Equations, Vol. 2016 (2016), No. 268, pp. 1-19.

Lyapunov-Sylvesters operators for (2+1)-Boussinesq equation

Abdelhamid Bezia, Anouar Ben Mabrouk, Kamel Betina

Abstract:
This article studies a technique for solving a two-dimensional Boussinesq equation discretized using a finite difference method. It consists of an order reduction method into a coupled system of second-order equations, and to formulate the fully discretized, implicit time-marched system as a Lyapunov-Sylvester matrix equation. Convergence and stability is examined using Lyapunov criterion and manipulating generalized Lyapunov-Sylvester operators. Some numerical implementations are provided at the end to validate the theoretical results.

Submitted February 8, 2016. Published October 7, 2016.
Math Subject Classifications: 65M06, 65M12, 65M22, 15A30, 37B25.
Key Words: Boussinesq equation; finite difference method; Numerical solution; Lyapunov-Sylvester operators.

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Abdelhamid Bezia
Algebra and Number Theory Laboratory
Faculty of Mathematics
University of Sciences and Technology Houari Boumediene
BP 32 EL-Alia 16111, Bab Ezzouar, Algiers, Algeria
email: abdelhamid.bezia@gmail.com
Anouar Ben Mabrouk
Département de Mathématiques
Institut Supérieur de Mathámatiques Appliquées et Informatique de Kairouan
Avenue Assad Ibn Al-Fourat, Kairouan 3100, Tunisia
email: anouar.benmabrouk@fsm.rnu.tn
Kamel Betina
Algebra and Number Theory Laboratory
Faculty of Mathematics
University of Sciences and Technology Houari Boumediene
BP 32 EL-Alia 16111, Bab Ezzouar, Algiers, Algeria
email: kamelbetina@gmail.com

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