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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/47996/1/ACCN15-Bangkok-Analytical_approximate_solutions_of_the_duffing-relativistic_oscillator.pdf
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spelling my.iium.irep.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 REM 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
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
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/47996/1/ACCN15-Bangkok-Analytical_approximate_solutions_of_the_duffing-relativistic_oscillator.pdf
http://irep.iium.edu.my/47996/
_version_ 1643613293398458368
score 13.211869

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