On the reduction of non-linear oscillator-equations to Abel forms

Markakis, MP

dc.contributor.author	Markakis, MP	en
dc.date.accessioned	2014-03-01T01:21:10Z
dc.date.available	2014-03-01T01:21:10Z
dc.date.issued	2004	en
dc.identifier.issn	0096-3003	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16116
dc.subject	Non-linear ODEs	en
dc.subject	Non-linear oscillators	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Analytical solutions	en
dc.subject.other	Non-linear ODEs	en
dc.subject.other	Non-linear oscillations	en
dc.subject.other	Van der pol equations	en
dc.subject.other	Asymptotic stability	en
dc.subject.other	Functions	en
dc.subject.other	Integral equations	en
dc.subject.other	Mathematical models	en
dc.subject.other	Mathematical transformations	en
dc.subject.other	Problem solving	en
dc.subject.other	Differential equations	en
dc.title	On the reduction of non-linear oscillator-equations to Abel forms	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.amc.2003.08.038	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.amc.2003.08.038	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	The particular ordinary differential equations (ODEs) governing some specific nonlinear oscillators are reduced to equivalent Abel equations by means of a series of functional transformations. These equivalent equations do not accept analytical solutions in terms of tabulated functions. So, the results of this work combined with the non-existence of exact solutions in the literature lead to the speculation that we need to construct new analytical functions in order to confront particular non-linearities in mechanical oscillations and physical problems generally. (C) 2003 Elsevier Inc. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE INC	en
heal.journalName	Applied Mathematics and Computation	en
dc.identifier.doi	10.1016/j.amc.2003.08.038	en
dc.identifier.isi	ISI:000224276900006	en
dc.identifier.volume	157	en
dc.identifier.issue	2	en
dc.identifier.spage	357	en
dc.identifier.epage	368	en