Lyapunov-Sylvester operators for Kuramoto-Sivashinsky Equation
Numerical Analysis
2015-11-10 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1511.02368,
title = {Lyapunov-Sylvester operators for Kuramoto-Sivashinsky Equation},
author = {Abdelhamid Bezia and Anouar Ben Mabrouk},
journal= {arXiv preprint arXiv:1511.02368},
year = {2015}
}
Comments
18 pages