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

Eunjung Lee, Dojin Kim

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish
Pages (from-to)16349-16365
Number of pages17
JournalAIMS Mathematics
Volume7
Issue number9
DOIs
StatePublished - 2022

Keywords

  • finite difference method
  • linearization scheme
  • nonlinear Schrödinger equation
  • stability

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