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Approximate Solutions of Second and Fourth Order Ordinary Differential Systems with Strong Generalized Nonlinearity

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dc.contributor.advisor Uddin, Dr. Md. Alhaz
dc.contributor.author Ullah, Md. Wali
dc.date.accessioned 2018-08-14T04:51:19Z
dc.date.available 2018-08-14T04:51:19Z
dc.date.copyright 2013
dc.date.issued 2013-12
dc.identifier.other ID 1151502
dc.identifier.uri http://hdl.handle.net/20.500.12228/386
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, December 2013. en_US
dc.description Cataloged from PDF Version of Thesis.
dc.description Includes bibliographical references (pages 41-48).
dc.description.abstract A perturbation method known as "the asymptotic averaging method" in the theory of nonlinear oscillations was first presented by Krylov and Bogoliubov (KB) in 1947. Primarily, the method was developed only to obtain the periodic solutions of second order weakly nonlinear differential systems. Later, the method of KB has been improved and justified by Bogoliubov and Mitropolskii in 1967. In literature, this method is known as the Krylov-Bogoliubov-Mitropolskii (KBM) method. Now a days, this method is used for obtaining the solutions of second, third and fourth order weakly nonlinear differential systems for oscillatory, damped oscillatory, over damped, critically damped and more critically damped cases by imposing some special restrictions. Ji-Huan He has developed a homotopy perturbation method for solving second order strongly nonlinear differential systems without damping. Uddin ci al. have presented an approximate analytical technique for second order strongly nonlinear differential systems with damping by combining He's homotopy perturbation technique and the extended form of the KBM method. Recently, Uddin ci al. have developed an analytical approximate technique for solving a certain type of fourth order strongly nonlinear oscillatory differential systems with small damping and cubic nonlinearity by combining He's homotopy perturbation and the extended form of the KBM methods. In this thesis, approximate analytical techniques shall be presented by combining the He's homotopy perturbation technique and the extended form of the KBM method for solving the second and fourth order nonlinear ordinary differential systems with strong generalized nonlinearity. To justify the presented methods, the approximate solutions have been compared to those solutions obtained by the fourth order Runge-Kutta method. en_US
dc.description.statementofresponsibility Md. Wali Ullah
dc.format.extent 48 pages
dc.language.iso en_US en_US
dc.publisher Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh. en_US
dc.subject Differential Systems en_US
dc.subject Approximate Solutions en_US
dc.subject Runge-Kutta Method en_US
dc.title Approximate Solutions of Second and Fourth Order Ordinary Differential Systems with Strong Generalized Nonlinearity en_US
dc.type Thesis en_US
dcterms.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.description.degree Master of Philosophy in Mathematics
dc.contributor.department Department of Mathematics


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