On an efficient k-step iterative method for nonlinear equations

  1. Amat, S. 1
  2. Bermúdez, C. 1
  3. Hernández-Verón, M.A. 2
  4. Martínez, E. 3
  1. 1 Universidad Politécnica de Cartagena

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

  2. 2 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  3. 3 Universidad Politécnica de Valencia

    Universidad Politécnica de Valencia

    Valencia, España

    ROR https://ror.org/01460j859

Journal of Computational and Applied Mathematics

ISSN: 0377-0427

Year of publication: 2016

Volume: 302

Pages: 258-271

Type: Article

DOI: 10.1016/J.CAM.2016.02.003 SCOPUS: 2-s2.0-84959511037 WoS: WOS:000374601100019 GOOGLE SCHOLAR

More publications in: Journal of Computational and Applied Mathematics


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.