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 language | English |
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Pages (from-to) | 16349-16365 |
Number of pages | 17 |
Journal | AIMS Mathematics |
Volume | 7 |
Issue number | 9 |
DOIs | |
State | Published - 2022 |
Keywords
- finite difference method
- linearization scheme
- nonlinear Schrödinger equation
- stability