KUET Institutional Repository

Analytical Solutions of Third and Fourth Order Weakly Nonlinear Ordinary Differential Systems with Damping and Slowly Varying Coefficients by the Unified KBM Method

Show simple item record

dc.contributor.advisor Uddin, Prof. Dr. Md. Alhaz
dc.contributor.author Ali, Md. Eabad
dc.date.accessioned 2018-08-14T08:43:24Z
dc.date.available 2018-08-14T08:43:24Z
dc.date.copyright 2015
dc.date.issued 2015-06
dc.identifier.other ID 1251554
dc.identifier.uri http://hdl.handle.net/20.500.12228/392
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, June 2015. en_US
dc.description Cataloged from PDF Version of Thesis.
dc.description Includes bibliographical references (pages 44-50).
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 the second order weakly nonlinear differential systems. Later, the method of KB has been improved and justified by Bogoliubov and Mitropolaskii in 1967. In literature, this method is known as the Krylov- Bogoliubov-Mitropolaskii (KBM) method. Now a days this method is used for obtaining the solutions of second, third and fourth order nonlinear differential systems for oscillatory, damped oscillatory, over damped, critically damped and more critically damped cases by imposing some proper restrictions, in this thesis, an analytical approximate technique is extended to find out the second approximate solutions of third order weakly nonlinear differential systems in the presence of strong linear damping and slowly varying coefficients based on the KBM method. Also, the KBM method is presented to fmd out the solutions of a fourth order weakly nonlinear differential systems in the presence of strong linear damping and slowly varying coefficients including some limitations. To justify the presented method, the approximate solutions have been compared to those solutions obtained by the fourth order Runge-Kutta method graphically. en_US
dc.description.statementofresponsibility Md. Eabad Ali
dc.format.extent 50 pages
dc.language.iso en_US en_US
dc.publisher Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh. en_US
dc.subject Third and Fourth Order Weakly Nonlinear Ordinary Differential Systems en_US
dc.subject Unified KBM Method en_US
dc.subject Runge-Kutta Method en_US
dc.title Analytical Solutions of Third and Fourth Order Weakly Nonlinear Ordinary Differential Systems with Damping and Slowly Varying Coefficients by the Unified KBM Method 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


Files in this item

This item appears in the following Collection(s)

Show simple item record

Search KUET IR


Advanced Search

Browse

My Account

Statistics