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AIMS Mathematics

2022, Volume 7, Issue 9: 16349-16365. doi: 10.3934/math.2022893
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Stability analysis of the implicit finite difference schemes for nonlinear Schrödinger equation

  • 1.
    School of Mathematics and Computing, Yonsei University, Seoul, 03722, Korea
  • 2.
    Department of Mathematics, Dongguk University, Seoul, 04620, Korea
  • Received: 06 May 2022 Revised: 23 June 2022 Accepted: 29 June 2022 Published: 05 July 2022

  • MSC : 65M06, 65M12

  • 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.

    Citation: Eunjung Lee, Dojin Kim. Stability analysis of the implicit finite difference schemes for nonlinear Schrödinger equation[J]. AIMS Mathematics, 2022, 7(9): 16349-16365. doi: 10.3934/math.2022893

    Related Papers:

  • 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.


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