TY  - JOUR
AU  - Lee, Eunjung
AU  - Kim, Dojin
PY  - 2022
TI  - Stability analysis of the implicit finite difference schemes for nonlinear Schrödinger equation
JO  - AIMS Mathematics
SP  - 16349
EP  - 16365
VL  - 7
IS  - 9
AB  - 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.
UR  - https://doi.org/10.3934/math.2022893
DO  - 10.3934/math.2022893