Lyapunov-Sylvester Operators for Numerical Solutions of NLS Equation
Numerical Analysis
2015-11-10 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1511.02358,
title = {Lyapunov-Sylvester Operators for Numerical Solutions of NLS Equation},
author = {Riadh Chteoui and Anouar Ben Mabrouk and Hichem Ounaies},
journal= {arXiv preprint arXiv:1511.02358},
year = {2015}
}
Comments
18 pages