An extension of the general Struble's method for solving an \(n\)th order nonlinear differential equation when the corresponding unperturbed equation has some repeated eigenvalues
type: Item
instance of: scholarly article
title: An extension of the general Struble's method for solving an \(n\)th order nonlinear differential equation when the corresponding unperturbed equation has some repeated eigenvalues
zbMATH Open document ID: 1173.34002
author: M. Adul Kalam Azad
author: Kamalesh Chandra Roy
author: M. Majedur Rahman
author: M. Shamsul Alam
published in: Journal of the Franklin Institute
publication date: 2009-05-12T00:00:00Z
review text: The authors show that the extended general Struble's technique is more suitable than the unified Krylov-Bogoliubov-Mitropolskii (KBM) method in solving problems that occur in critical conditions. First, the method is illustrated by the fourth-order nonlinear differential equation of the form \[ x^{(4)} + c_1 {x}''' + c_2 {x}'' + c_3 {x}' + c_4 x = - \varepsilon x^3, \] whose unperturbed equation has repeated complex eigenvalues. Second, a steady-state solution is also determined for the following fourth order nonlinear and non-autonomous equation of the form \[ x^{(4)} + c_1 {x}''' + c_2 {x}'' + c_3 {x}' + c_4 x = - \varepsilon x^3 + \varepsilon E\cos vt. \] Further, a critical condition is investigated when two real eigenvalues of the unperturbed equation are non-positive and equal. Some numerical examples are also given.
reviewed by: Cemil Tunç
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 5552686
zbMATH Keywords: Struble's method
zbMATH Keywords: \(n\)th order nonlinear differential equation
MaRDI profile type: Publication
full work available at URL: j.jfranklin.2008.06.010
OpenAlex ID: W2079993604
Wikidata QID: Q115346473
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DOI: 10.1016/J.JFRANKLIN.2008.06.010
description: scientific article; zbMATH DE number 5552686