2015/11/07 by Abdelhamid Bezia, Bezia, Abdelhamid, Anouar Ben Mabrouk +1
Computer Science · Engineering · Mathematics · #15A30 #37B25 #65M06 #65M12 #65M22 #F.2.1 #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Numerical Analysis (math.NA) #Numerical methods for differential equations #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1511.02368
openalex publication_date 2015/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A numerical method is developed leading to algebraic systems based on generalized Lyapunov-Sylvester operators to approximate the solution of two-dimensional Kuramoto-Sivashinsky equation. It consists of an order reduction method and a finite difference discretization which is proved to be uniquely solvable, stable and convergent by using Lyapunov criterion and manipulating generalized Lyapunov-Sylvester operators. Some numerical implementations are provided at the end to validate the theoretical results.