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
Year of publication: 2016
Volume: 302
Pages: 258-271
Type: Article
More publications in: Journal of Computational and Applied Mathematics
Abstract
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.