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Ball Comparison between Three Sixth Order Methods for Banach Space Valued Operators

2020Journal article Open access
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dc.contributor.authorBehl, Ramandeep
dc.contributor.authorArgyros, Ioannis K.
dc.contributor.authorMachado, J. A. Tenreiro
dc.date.accessioned2022-01-12T14:22:57Z
dc.date.available2022-01-12T14:22:57Z
dc.date.issued2020
dc.description.abstractThree methods of sixth order convergence are tackled for approximating the solution of an equation defined on the finitely dimensional Euclidean space. This convergence requires the existence of derivatives of, at least, order seven. However, only derivatives of order one are involved in such methods. Moreover, we have no estimates on the error distances, conclusions about the uniqueness of the solution in any domain, and the convergence domain is not sufficiently large. Hence, these methods have limited usage. This paper introduces a new technique on a general Banach space setting based only the first derivative and Lipschitz type conditions that allow the study of the convergence. In addition, we find usable error distances as well as uniqueness of the solution. A comparison between the convergence balls of three methods, not possible to drive with the previous approaches, is also given. The technique is possible to use with methods available in literature improving, consequently, their applicability. Several numerical examples compare these methods and illustrate the convergence criteria.pt_PT
dc.description.sponsorshipThis project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, Saudi Arabia, under Grant No. D-540-130-1441. The authors, therefore, acknowledge with thanks DSR for technical and financial support.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.doi10.3390/math8050667pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.22/19433
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherMDPIpt_PT
dc.relationD-540-130-1441pt_PT
dc.relation.publisherversionhttps://www.mdpi.com/2227-7390/8/5/667pt_PT
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/pt_PT
dc.subjectBanach spacept_PT
dc.subjectLocal convergencept_PT
dc.subjectSystem of nonlinear equationspt_PT
dc.subjectIterative methodspt_PT
dc.titleBall Comparison between Three Sixth Order Methods for Banach Space Valued Operatorspt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.issue5pt_PT
oaire.citation.startPage667pt_PT
oaire.citation.titleMathematicspt_PT
oaire.citation.volume8pt_PT
person.familyNameTenreiro Machado
person.givenNameJ. A.
person.identifier.ciencia-id7A18-4935-5B29
person.identifier.orcid0000-0003-4274-4879
person.identifier.ridM-2173-2013
person.identifier.scopus-author-id55989030100
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication82cd5c17-07b6-492b-b3e3-ecebdad1254f
relation.isAuthorOfPublication.latestForDiscovery82cd5c17-07b6-492b-b3e3-ecebdad1254f

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