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 |
|---|---|
| Pages (from-to) | 16349-16365 |
| Number of pages | 17 |
| Journal | AIMS Mathematics |
| Volume | 7 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 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)