Numerical approximations and asymptotic limits of some nonlinear problems

Authors

  • A. Ben Mabrouk University of Tabuk, Saudi Arabia
  • A. Bezia University of Sciences and Technology Houari Boumediene, Algeria
  • C. Soussi University of Sfax, Tunisia

DOI:

https://doi.org/10.31926/but.mif.2023.3.65.2.5

Keywords:

NLS equation, Numerical solutions, Finite difference, Von Neumann Stability, Convergence, Consistency, Error estimates, Asymptotic limits

Abstract

In the present work, a numerical approach is dedicated to the approximation to the solutions of a time-independent nonlinear Schr¨odinger equation in a mixed case provided with numerical tests on the asymptotic limits of the solution according to some parameters. A finite difference discretization with calibrations is applied leading to a quasi-linear algebraic system. where the its solvability is investigated as well as its stability and convergence via Von Neumann method. Some numerical experiments are developed to validate the result, and to test the effect of some parameters on the asymptotic limit of the problem.

Author Biographies

A. Ben Mabrouk, University of Tabuk, Saudi Arabia

Department of Mathematics, Faculty of Science, King Faisal Road, 47512 Tabuk;
University of Monastir
Laboratory of Algebra, Number Theory and Nonlinear Analysis, Department of Mathematics, Faculty of Sciences, Avenue of the Environment, 5019 Monastir, Tunisia. e-mail: anouar.benmabrouk@fsm.rnu.tn;
University of Kairouan
Department of Mathematics, Higher Institute of Applied Mathematics and Computer Science, Street of Assad Ibn Alfourat, 3100 Kairouan, Tunisia

A. Bezia, University of Sciences and Technology Houari Boumediene, Algeria

Laboratory of Algebra and Number Theory, BP 32 Bab Ezzouar, 16111 Algiers;
National Higher School of Mathematics, Scientific and Technology Hub of Sidi Abdellah, Algeria
P.O. Box 75, Algiers 16093

C. Soussi, University of Sfax, Tunisia

Department of Mathematics, Faculty of Sciences of Sfax, 3000 Sfax, e-mail: chouhaid.souissi@fss.usf.tn

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Published

2023-12-18

Issue

Vol. 3(65) No. 2 (2023)

Section

MATHEMATICS