On the efficiency of Newton and Broyden numerical methods in the investigation of the regular polygon problem of (N + 1) bodies

Gousidou-Koutita, M; Kalvouridis, TJ

dc.contributor.author	Gousidou-Koutita, M	en
dc.contributor.author	Kalvouridis, TJ	en
dc.date.accessioned	2014-03-01T01:31:34Z
dc.date.available	2014-03-01T01:31:34Z
dc.date.issued	2009	en
dc.identifier.issn	0096-3003	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19819
dc.subject	(N + 1)-Ring-body problem	en
dc.subject	Celestial Mechanics	en
dc.subject	Comparison of numerical methods	en
dc.subject	Newton and quasi-Newton methods	en
dc.subject	Non-linear algebraic equations	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	(N + 1)-Ring-body problem	en
dc.subject.other	Celestial Mechanics	en
dc.subject.other	Comparison of numerical methods	en
dc.subject.other	Newton and quasi-Newton methods	en
dc.subject.other	Non-linear algebraic equations	en
dc.subject.other	Astrophysics	en
dc.subject.other	Mechanics	en
dc.subject.other	Newton-Raphson method	en
dc.subject.other	Number theory	en
dc.subject.other	Numerical methods	en
dc.title	On the efficiency of Newton and Broyden numerical methods in the investigation of the regular polygon problem of (N + 1) bodies	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.amc.2009.02.015	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.amc.2009.02.015	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	Numerical methods of finding the roots of a system of non-linear algebraic equations are treated in this paper. This paper attempts to give an answer to the selection of the most efficient method in a complex problem of Celestial Dynamics, the so-called ring problem of (N + 1) bodies. We apply Newton and Broyden's method to these problems and we investigate, by means of their use, the planar equilibrium points, the five equilibrium zones, which are symbolized by A(1), A(2), B, C-2, and C-1 (by order of appearance from the center O to the periphery of the imaginary circle on which the primaries lie) [T. J. Kalvouridis, A planar case of the N + 1 body problem: the ring problem. Astrophys. Space Sci. 260 (3) (1999) 309-325], and the attracting regions of the system. The efficiency of these methods is studied through a comparative process. The obtained results are demonstrated in figures and are discussed. (c) 2009 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.2009.02.015	en
dc.identifier.isi	ISI:000265783800012	en
dc.identifier.volume	212	en
dc.identifier.issue	1	en
dc.identifier.spage	100	en
dc.identifier.epage	112	en