A Generalized Lyapunov-Sylvester Computational Method for Numerical Solutions of NLS Equation with Singular Potential

作     者：Riadh Chteoui Anouar Ben Mabrouk 

作者机构：Departement de Mathmatiques Facult des Sciences de TunisUniversit de Tunis ElManar UR11ES50–Algebra Number Theory and Nonlinear Analysis Department ofMathematics Faculty of Sciences Monastir University Department of Mathematics Higher Institute of Applied Mathematics andInformatics Street of Assad Ibn Alfourat Kairouan University Department of Mathematics College of Sciences University of Tabuk 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2017年第33卷第4期

页      面：333-354页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

主　　题：NLS equation finite-difference scheme stability analysis Lyapunov criterion con-sistency convergence error estimates Lyapunov operator. 

摘      要：In the present paper a numerical method is developed to approximate the solution of two-dimensional Nonlinear Schrodinger equation in the presence of a sin- gular potential. The method leads to generalized Lyapunov-Sylvester algebraic opera- tors that are shown to be invertible using original topological and differential calculus issued methods. The numerical scheme is proved to be consistent, convergent and sta- ble using the Lyapunov criterion, lax equivalence theorem and the properties of the generalized Lyapunov-Sylvester operators.