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
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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
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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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