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On Some Asymptotic Solutions of Fourth Order Critically Damped Nonlinear Systems

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dc.contributor.advisor Rahman, Prof. Dr. Fouzia
dc.contributor.author Haque, B. M. Ikramul
dc.date.accessioned 2018-08-13T08:09:38Z
dc.date.available 2018-08-13T08:09:38Z
dc.date.copyright 2008
dc.date.issued 2008-01
dc.identifier.other ID 0151504
dc.identifier.uri http://hdl.handle.net/20.500.12228/361
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, January 2008. en_US
dc.description Cataloged from PDF Version of Thesis.
dc.description Includes bibliographical references (pages 59-68).
dc.description.abstract Krylov and Bogoliubov introduced a perturbation method named "asymptotic averaging method". The method was developed only to obtain the periodic solution of second order nonlinear differential systems. Now the method is used to obtain the solutions of oscillatory, damped oscillatory, over-damped, critically damped and more critically damped systems with of second, third, fourth etc. order nonlinear differential equations by imposing some restrictions to make the solutions uniformly valid. The method of Krylov and Bogoliubov has been improved and justified by Bogoliubov and Mitropolskii. In this dissertation, we have modified and extended the Krylov-Bogoliubov-Mitropolskii (KBM) method to investigate the fourth order critically damped and more critically damped nonlinear systems. We have imposed some restrictions on the eigenvalues to determine the unknown functions which are related to the variational equations. To get the solutions of the variational equations, we have replaced the variables by their corresponding linear values. For justification of the solution obtained by the extended KBM method, we have compared the results to those obtained by the fourth order Runge-Kutta method. en_US
dc.description.statementofresponsibility B. M. Ikramul Haque
dc.format.extent 68 pages
dc.language.iso en_US en_US
dc.publisher Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh. en_US
dc.subject Asymptotic Solutions en_US
dc.subject Asymptotic Averaging Method en_US
dc.title On Some Asymptotic Solutions of Fourth Order Critically Damped Nonlinear Systems 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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