Analytical approximate solutions of the duffing-relativistic oscillator

The aim of this paper is to use high-order harmonic balance method (HBM) as a novel solution procedure for investigation of the Duffing-relativistic oscillation. Usually, a set of complex nonlinear algebraic equations is appeared when HBM is applied. Investigating analytically for such kind of compl...

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Main Authors:	Chowdhury, Md. Sazzad Hossien, Motakabber, S. M. A.
Format:	Conference or Workshop Item
Language:	English
Published:	2015
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/47996/ http://irep.iium.edu.my/47996/ http://irep.iium.edu.my/47996/1/ACCN15-Bangkok-Analytical_approximate_solutions_of_the_duffing-relativistic_oscillator.pdf

id	iium-47996
recordtype	eprints
spelling	iium-479962016-05-23T02:58:40Z http://irep.iium.edu.my/47996/ Analytical approximate solutions of the duffing-relativistic oscillator Chowdhury, Md. Sazzad Hossien Motakabber, S. M. A. QA Mathematics The aim of this paper is to use high-order harmonic balance method (HBM) as a novel solution procedure for investigation of the Duffing-relativistic oscillation. Usually, a set of complex nonlinear algebraic equations is appeared when HBM is applied. Investigating analytically for such kind of complex nonlinear algebraic equations is tremendously difficult and cumbersome. In the present study, a small parameter is found, for which the power series solutions produces desired results. The obtained results are evaluated by comparing with the exact solutions computed numerically. The effect of initial conditions in the nonlinear natural frequencies is carried out and it is proved the proposed method is not only simple, but also more reliable for analysis for the Duffing-relativistic oscillator. The method is mainly illustrated in strongly nonlinear Duffing-relativistic oscillator, but it can be widely applicable in other problems arising nonlinear sciences and engineering. 2015-12-28 Conference or Workshop Item NonPeerReviewed application/pdf en http://irep.iium.edu.my/47996/1/ACCN15-Bangkok-Analytical_approximate_solutions_of_the_duffing-relativistic_oscillator.pdf Chowdhury, Md. Sazzad Hossien and Motakabber, S. M. A. (2015) Analytical approximate solutions of the duffing-relativistic oscillator. In: The Third Intl. Conf. On Advances in Computing, Control and Networking-ACCN 2015, 28--29 December 2015, Bangkok, Thailand . 10.15224/ 978-1-63248-082-8-14
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Chowdhury, Md. Sazzad Hossien Motakabber, S. M. A. Analytical approximate solutions of the duffing-relativistic oscillator
description	The aim of this paper is to use high-order harmonic balance method (HBM) as a novel solution procedure for investigation of the Duffing-relativistic oscillation. Usually, a set of complex nonlinear algebraic equations is appeared when HBM is applied. Investigating analytically for such kind of complex nonlinear algebraic equations is tremendously difficult and cumbersome. In the present study, a small parameter is found, for which the power series solutions produces desired results. The obtained results are evaluated by comparing with the exact solutions computed numerically. The effect of initial conditions in the nonlinear natural frequencies is carried out and it is proved the proposed method is not only simple, but also more reliable for analysis for the Duffing-relativistic oscillator. The method is mainly illustrated in strongly nonlinear Duffing-relativistic oscillator, but it can be widely applicable in other problems arising nonlinear sciences and engineering.
format	Conference or Workshop Item
author	Chowdhury, Md. Sazzad Hossien Motakabber, S. M. A.
author_facet	Chowdhury, Md. Sazzad Hossien Motakabber, S. M. A.
author_sort	Chowdhury, Md. Sazzad Hossien
title	Analytical approximate solutions of the duffing-relativistic oscillator
title_short	Analytical approximate solutions of the duffing-relativistic oscillator
title_full	Analytical approximate solutions of the duffing-relativistic oscillator
title_fullStr	Analytical approximate solutions of the duffing-relativistic oscillator
title_full_unstemmed	Analytical approximate solutions of the duffing-relativistic oscillator
title_sort	analytical approximate solutions of the duffing-relativistic oscillator
publishDate	2015
url	http://irep.iium.edu.my/47996/ http://irep.iium.edu.my/47996/ http://irep.iium.edu.my/47996/1/ACCN15-Bangkok-Analytical_approximate_solutions_of_the_duffing-relativistic_oscillator.pdf
first_indexed	2023-09-18T21:08:12Z
last_indexed	2023-09-18T21:08:12Z
_version_	1777411076077387776

Analytical approximate solutions of the duffing-relativistic oscillator

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