TY - JOUR
T1 - Finite Difference Method for (2+1)-Kuramoto-Sivashinsky Equation
AU - Bezia , Abdelhamid
AU - Anouar , Ben Mabrouk
JO - Journal of Partial Differential Equations
VL - 3
SP - 193
EP - 213
PY - 2018
DA - 2018/09
SN - 31
DO - http://doi.org/10.4208/jpde.v31.n3.1
UR - https://global-sci.org/intro/article_detail/jpde/12703.html
KW - Kuramoto-Sivashinsky equation
KW - Finite difference method
KW - Lyapunov-Sylvester operators.
AB - <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>