Finite Difference Method for (2+1)-Kuramoto-Sivashinsky Equation

Authors

  • 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
  • Ben Mabrouk Anouar Département de Mathématiques, Institut Supérieur de Mathámatiques Appliquées et Informatique de Kairouan, Avenue Assad Ibn Al-Fourat, Kairouan 3100, Tunisia

DOI:

https://doi.org/10.4208/jpde.v31.n3.1

Keywords:

Kuramoto-Sivashinsky equation;Finite difference method;Lyapunov-Sylvester operators.

Abstract

This paper investigates a solution technique for solving a two-dimensional Kuramoto-Sivashinsky 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.

Published

2018-09-20

Issue

Section

Articles

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