Numerical solution of nonlinear Schrodinger equation using Crank-Nicolson method

The nonlinear Schrödinger equations (NLS) are used in modeling several physical phenomena such as Bose-Einstein condensation, laser beam transmissions, deep water turbulence, and solitary wave propagation in optical fibers. Solving NLS equation resulting in a wave function that makes it easier to ex...

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Main Author:	Uddin, Md. Noman
Format:	Thesis
Language:	English
Published:	2020
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/102598/1/MdNomanUddinMFS2020.pdf.pdf
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id	my-utm-ep.102598
record_format	uketd_dc
spelling	my-utm-ep.1025982023-09-09T01:49:23Z Numerical solution of nonlinear Schrodinger equation using Crank-Nicolson method 2020 Uddin, Md. Noman QA Mathematics The nonlinear Schrödinger equations (NLS) are used in modeling several physical phenomena such as Bose-Einstein condensation, laser beam transmissions, deep water turbulence, and solitary wave propagation in optical fibers. Solving NLS equation resulting in a wave function that makes it easier to examine the behavior and performance of physical systems or chemical reactions. There are several methods that can be used to solve the nonlinear Schrödinger equation. In this study, one dimensional nonlinear Schrödinger equation was solved by Crank-Nicolson method with Dirichlet boundary condition and symmetric cyclic tridiagonal matrix using MATLAB. The Crank-Nicolson scheme is used as it is one of the adaptable, fast, and robust techniques for integrating the time-dependent Schrödinger equation. In addition, the operational framework for finite difference scheme and stability analysis for this technique are presented. Lastly, the performance of the Crank-Nicolson scheme is analyzed by computing the error between the estimated and the exact solution. It is shown that both results from numerical scheme and exact solution have good agreement. 2020 Thesis http://eprints.utm.my/102598/ http://eprints.utm.my/102598/1/MdNomanUddinMFS2020.pdf.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:146337 masters Universiti Teknologi Malaysia Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Uddin, Md. Noman Numerical solution of nonlinear Schrodinger equation using Crank-Nicolson method
description	The nonlinear Schrödinger equations (NLS) are used in modeling several physical phenomena such as Bose-Einstein condensation, laser beam transmissions, deep water turbulence, and solitary wave propagation in optical fibers. Solving NLS equation resulting in a wave function that makes it easier to examine the behavior and performance of physical systems or chemical reactions. There are several methods that can be used to solve the nonlinear Schrödinger equation. In this study, one dimensional nonlinear Schrödinger equation was solved by Crank-Nicolson method with Dirichlet boundary condition and symmetric cyclic tridiagonal matrix using MATLAB. The Crank-Nicolson scheme is used as it is one of the adaptable, fast, and robust techniques for integrating the time-dependent Schrödinger equation. In addition, the operational framework for finite difference scheme and stability analysis for this technique are presented. Lastly, the performance of the Crank-Nicolson scheme is analyzed by computing the error between the estimated and the exact solution. It is shown that both results from numerical scheme and exact solution have good agreement.
format	Thesis
qualification_level	Master's degree
author	Uddin, Md. Noman
author_facet	Uddin, Md. Noman
author_sort	Uddin, Md. Noman
title	Numerical solution of nonlinear Schrodinger equation using Crank-Nicolson method
title_short	Numerical solution of nonlinear Schrodinger equation using Crank-Nicolson method
title_full	Numerical solution of nonlinear Schrodinger equation using Crank-Nicolson method
title_fullStr	Numerical solution of nonlinear Schrodinger equation using Crank-Nicolson method
title_full_unstemmed	Numerical solution of nonlinear Schrodinger equation using Crank-Nicolson method
title_sort	numerical solution of nonlinear schrodinger equation using crank-nicolson method
granting_institution	Universiti Teknologi Malaysia
granting_department	Faculty of Science
publishDate	2020
url	http://eprints.utm.my/102598/1/MdNomanUddinMFS2020.pdf.pdf
_version_	1783729189893963776

Numerical solution of nonlinear Schrodinger equation using Crank-Nicolson method

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