KUET Institutional Repository

Approximate Solution Techniques for Fourth Order Nonlinear Ordinary Differential Systems

Show simple item record

dc.contributor.advisor Uddin, Dr. Md. Alhaz
dc.contributor.author Alom, Md. Asraful
dc.date.accessioned 2018-08-14T03:55:12Z
dc.date.available 2018-08-14T03:55:12Z
dc.date.copyright 2012
dc.date.issued 2012-12
dc.identifier.other ID 1051506
dc.identifier.uri http://hdl.handle.net/20.500.12228/381
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 2012. en_US
dc.description Cataloged from PDF Version of Thesis.
dc.description Includes bibliographical references (pages 40-46).
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 nonlinear differential systems for oscillatory, damped oscillatory, over damped, critically damped and more critically damped cases by imposing some restrictions. Ji-Huan He has developed a homotopy perturbation method for second order strongly nonlinear differential systems without damping. Recently, Uddin el al. have developed approximate analytical technique for second order strongly nonlinear differential systems with damping combining He's homotopy perturbation technique and the extended form of the KBM method. In this thesis, an analytical approximate technique will be presented by combining the He's hornotopy perturbation technique and the extended form of the KBM method for solving certain type of fourth order strongly nonlinear differential systems with small damping and cubic nonlinearity. Also, the KBM method will be modified and elaborated to find out the solutions of fourth order weakly and near critically damped nonlinear differential systems by imposing some restrictions on the eigen values. To justify the presented methods, the approximate solutions have been compared to those solutions obtained by the fourth order Runge-Kuttu method. en_US
dc.description.statementofresponsibility Md. Asraful Alom
dc.format.extent 46 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 Nonlinear Ordinary Differential Systems en_US
dc.subject Runge-Kutta Method en_US
dc.title Approximate Solution Techniques for Fourth Order Nonlinear Ordinary Differential Systems en_US
dc.type Thesis en_US
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


Browse

My Account

Statistics