Stability analysis of the implicit finite difference schemes for nonlinear Schrödinger equation

AIMS Mathematics

article

Eunjung Lee¹  Dojin Kim² 

[1] School of Mathematics and Computing, Yonsei University;Department of Mathematics, Dongguk University

关键词: nonlinear Schrödinger equation;    stability;    linearization scheme;    finite difference method;   

DOI  :  10.3934/math.2022893

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY