@Article{JPDE-31-193,
author = {Bezia , Abdelhamid and Anouar , Ben Mabrouk},
title = {Finite Difference Method for (2+1)-Kuramoto-Sivashinsky Equation},
journal = {Journal of Partial Differential Equations},
year = {2018},
volume = {31},
number = {3},
pages = {193--213},
abstract = {<p>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.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v31.n3.1},
url = {http://global-sci.org/intro/article_detail/jpde/12703.html}
}