@article{Lee2022, 
author = {Eunjung Lee and Dojin Kim},
title = {Stability analysis of the implicit finite difference schemes for nonlinear Schrödinger equation},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {9},
pages = {16349-16365},
keywords = {nonlinear Schrödinger equation, stability, linearization scheme, finite difference method},
url = {https://www.sciopen.com/article/10.3934/math.2022893},
doi = {10.3934/math.2022893},
abstract = {This paper analyzes the stability of numerical solutions for a nonlinear Schrödinger equation that is widely used in several applications in quantum physics, optical business, etc. One of the most popular approaches to solving nonlinear problems is the application of a linearization scheme. In this paper, two linearization schemes—Newton and Picard methods were utilized to construct systems of linear equations and finite difference methods. Crank-Nicolson and backward Euler methods were used to establish numerical solutions to the corresponding linearized problems. We investigated the stability of each system when a finite difference discretization is applied, and the convergence of the suggested approximation was evaluated to verify theoretical analysis.}
}