Lyapunov-Sylvester operators for Kuramoto-Sivashinsky Equation
Abdelhamid Bezia, Anouar Ben Mabrouk
TL;DR
This paper introduces a numerical method using Lyapunov-Sylvester operators to solve the 2D Kuramoto-Sivashinsky equation, demonstrating stability, convergence, and practical effectiveness through numerical tests.
Contribution
It develops a novel algebraic approach based on generalized Lyapunov-Sylvester operators for solving the Kuramoto-Sivashinsky equation, including stability and convergence proofs.
Findings
Method is proven to be uniquely solvable, stable, and convergent.
Numerical implementations validate theoretical results.
Approach effectively approximates solutions of the 2D Kuramoto-Sivashinsky equation.
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.
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Taxonomy
TopicsNonlinear Dynamics and Pattern Formation · Stability and Controllability of Differential Equations · Numerical methods for differential equations