arXiv subjects

Abdelhamid Bezia

Publications and source records attributed to Abdelhamid Bezia.

2 recordsLinked to original sources

arXiv2015

Lyapunov-Sylvester operators for Kuramoto-Sivashinsky Equation

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.

math.NA↗

arXiv2015

Lyapunov-Sylvester Computational Method for Two-Dimensional Boussinesq Equation

A numerical method is developed leading to algebraic systems based on generalized Lyapunov-Sylvester operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference discretization. It is proved to be uniquely solvable, stable and convergent by using Lyapunov criterion and manipulating Lyapunov-Sylvester operators. Some numerical implementations are provided at the end of the paper to validate the theoretical results.

math.NA↗