Numerical investigation of the solutions of Schrödinger equation with exponential cubic B-spline finite element method-Reference-Cited by-同舟云学术

Numerical investigation of the solutions of Schrödinger equation with exponential cubic B-spline finite element method

Published:2020-12-17 Issue:2 Volume:22 Page:119-133
ISSN:1565-1339
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Ersoy Hepson Ozlem¹^ORCID,Dag Idris²

Affiliation:

1. Department of Mathematics and Computer Science, Faculty of Science and Letters, Eskisehir Osmangazi University , 26040 , Eskisehir , Turkey

2. Department of Computer Engineering , Faculty of Engineering and Architecture, Eskisehir Osmangazi University , 26040 , Eskisehir , Turkey

Abstract

Abstract In this paper, we investigate the numerical solutions of the cubic nonlinear Schrödinger equation via the exponential cubic B-spline collocation method. Crank–Nicolson formulas are used for time discretization of the target equation. A linearization technique is also employed for the numerical purpose. Four numerical examples related to single soliton, collision of two solitons that move in opposite directions, the birth of standing and mobile solitons and bound state solution are considered as the test problems. The accuracy and the efficiency of the purposed method are measured by max error norm and conserved constants. The obtained results are compared with the possible analytical values and those in some earlier studies.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modelling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2016-0179/pdf

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