Riadh Chteoui

Riadh Chteoui, Anouar Ben Mabrouk, Hichem Ounaies

In the present paper a numerical method is developed to approximate the solution of two-dimensional NLS equation in the presence of a singular potential. The method leads to Lyapunov-Syslvester algebraic operators that are shown to be invertible using original topological and differential calculus issued methods. The numerical scheme is proved to be consistent, convergent and stable using the based on Lyapunov criterion, lax equivalence theorem and the properties of the Lyapunov-Syslvester operators.

Anouar Ben Mabrouk, Riadh Chteoui

A numerical method is developed leading to Lyapunov 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 and analyzed for local truncation error for consistency. The stability is checked by using Lyapunov criterion and the convergence is studied. Some numerical implementations are provided at the end of the paper to validate the theoretical results.