On an efficient k-step iterative method for nonlinear equations
- Amat, S. 1
- Bermúdez, C. 1
- Hernández-Verón, M.A. 2
- Martínez, E. 3
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1
Universidad Politécnica de Cartagena
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2
Universidad de La Rioja
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3
Universidad Politécnica de Valencia
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ISSN: 0377-0427
Datum der Publikation: 2016
Ausgabe: 302
Seiten: 258-271
Art: Artikel
Andere Publikationen in: Journal of Computational and Applied Mathematics
Projekte im Zusammenhang
Zusammenfassung
This paper is devoted to the construction and analysis of an efficient k-step iterative method for nonlinear equations. The main advantage of this method is that it does not need to evaluate any high order Fréchet derivative. Moreover, all the k-step have the same matrix, in particular only one LU decomposition is required in each iteration. We study the convergence order, the efficiency and the dynamics in order to motivate the proposed family. We prove, using some recurrence relations, a semilocal convergence result in Banach spaces. Finally, a numerical application related to nonlinear conservative systems is presented. © 2016 Elsevier B.V. All rights reserved.