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Approximate Solution of the Quadratic Nonlinear Oscillator by Iteration Procedure

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dc.contributor.advisor Haque, Dr. B. M. Ikramul
dc.contributor.author Hossain, Md. Rakib
dc.date.accessioned 2018-08-08T06:36:34Z
dc.date.available 2018-08-08T06:36:34Z
dc.date.copyright 2015
dc.date.issued 2015-12
dc.identifier.other ID 0000000
dc.identifier.uri http://hdl.handle.net/20.500.12228/193
dc.description This thesis is submitted to the Department of Mathematics, Khulna University of Engineering & Technology in partial fulfillment of the requirements for the degree of Master of Science in Mathematics, December 2015. en_US
dc.description Cataloged from PDF Version of Thesis.
dc.description Includes bibliographical references (pages 28-34).
dc.description.abstract An analytical technique has been developed based on an iteration method to determine higher order approximate periodic solutions for a nonlinear oscillator with discontinuity for which the elastic force term anti-symmetric and quadratic. Usually, a set of nonlinear algebraic equations is solved with this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of large oscillations. A modified approximate analytic solution of the quadratic nonlinear oscillator "ẍ + x2 sgn(x) = 0" has been obtained based on an iteration procedure. Here we have used the truncated Fourier series in each iterative step. The approximate frequencies obtained by the technique shows a good agreement with the exact frequency and periodic solutions with the exact ones. The percentage of error between exact frequency and fourth approximate frequency of the method is as low as 0.00003%.The method is mainly illustrated by the quadratic nonlinear oscillator but it is also useful for many other nonlinear problems. en_US
dc.description.statementofresponsibility Md. Rakib Hossain
dc.format.extent 34 pages
dc.language.iso en_US en_US
dc.publisher Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh en_US
dc.rights Khulna University of Engineering & Technology (KUET) thesis/dissertation/internship reports are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission.
dc.subject Quadratic Nonlinear Oscillator en_US
dc.subject Fourier Series en_US
dc.subject Iterative Procedure en_US
dc.title Approximate Solution of the Quadratic Nonlinear Oscillator by Iteration Procedure en_US
dc.type Thesis en_US
dc.description.degree Master of Science in Mathematics
dc.contributor.department Department of Mathematics


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