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On Some Analytical Approximate Solutions of Fourth Order Damped Oscillatory and Near Critically Damped Nonlinear Systems

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dc.contributor.advisor Azad, Dr. Md. Abul Kalam
dc.contributor.author Rahman, Md. Habibur
dc.date.accessioned 2018-08-13T10:19:06Z
dc.date.available 2018-08-13T10:19:06Z
dc.date.copyright 2009
dc.date.issued 2009-03
dc.identifier.other ID 0651501
dc.identifier.uri http://hdl.handle.net/20.500.12228/369
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 Philosophy in Mathematics, March 2009. en_US
dc.description Cataloged from PDF Version of Thesis.
dc.description Includes bibliographical references (pages 55-60).
dc.description.abstract At first Krylov and Bogoliubov prcseflted a perturbation method known as the asymptotic averaging method' in the theory of nonlinear oscillations. Primarily, the method was proposed only to get the periodic solutions of second order autonomous systems with small nonlinearities. Later, the method has been extended by Bogoliubov and Mitropolskii. At present the method is used to obtain the solutions of second and higher order nonlinear equations for damped oscillatory, over damped, near critically damped, critically damped, more critically damped systems under some special conditions. The unified Krvlov-13ooliubov-Mitropolskii (KBM) method is used to find approximate solutions of fourth order nonlinear systems with large damping. In this thesis. the KBM method has been modified and elaborated to find out the solutions of' fourth order damped oscillatory and near critically damped non-oscillatory nonlinear systems by imposing some restrictions on the cigen-values. For verification of the results obtained by the modified KI3M method, we have compared them with those obtained by the fourth order Runge-Kutta method and a nice matching is observed. en_US
dc.description.statementofresponsibility Md. Habibur Rahman
dc.format.extent 60 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 Fourth Order Damped Oscillatory en_US
dc.subject Near Critically Damped Nonlinear en_US
dc.subject Runge-Kutta Method en_US
dc.title On Some Analytical Approximate Solutions of Fourth Order Damped Oscillatory and Near Critically Damped Nonlinear Systems en_US
dc.type Thesis en_US
dc.description.degree Master of Philosophy in Mathematics
dc.contributor.department Department of Mathematics

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