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

Eunjung Lee, Dojin Kim

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1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)16349-16365
Number of pages17
JournalAIMS Mathematics
Issue number9
Publication statusPublished - 2022

Bibliographical note

Funding Information:
This work was supported by The Laboratory of Computational Electromagnetics for Large-scale stealth platform (UD200047JD). The corresponding author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT)-(No. 2019R1C1C1003869). We appreciate Daae Kim for helping with the matrix computations in Newton iteration.

Publisher Copyright:
© 2022 Author(s), licensee AIMS Press.

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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