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Computational and Applied Mathematics

, Volume 35, Issue 1, pp 251–267 | Cite as

Some new bi-accelerator two-point methods for solving nonlinear equations

  • Alicia Cordero
  • Taher LotfiEmail author
  • Juan R. Torregrosa
  • Paria Assari
  • Katayoun Mahdiani
Article

Abstract

In this work, we extract some new and efficient two-point methods with memory from their corresponding optimal methods without memory, to estimate simple roots of a given nonlinear equation. Applying two accelerator parameters in each iteration, we try to increase the convergence order from four to seven without any new functional evaluation. To this end, firstly we modify three optimal methods without memory in such a way that we could generate methods with memory as efficient as possible. Then, convergence analysis is put forward. Finally, the applicability of the developed methods on some numerical examples is examined and illustrated by means of dynamical tools, both in smooth and in nonsmooth functions.

Keywords

Multi-point iterative methods With and without memory methods  Kung and Traub’s conjecture Efficiency index Dynamical plane Basin of attraction  Derivative-free method 

Mathematics Subject Classification

65B99 65H05 65Y20 41A25 

Notes

Acknowledgments

The authors thank to the anonymous referees for their suggestions to improve the final version of the paper. The second author would like to thank Hamedan Brach of Islamic Azad University for partial financial support in this research.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2014

Authors and Affiliations

  • Alicia Cordero
    • 1
  • Taher Lotfi
    • 2
    Email author
  • Juan R. Torregrosa
    • 1
  • Paria Assari
    • 2
  • Katayoun Mahdiani
    • 2
  1. 1.Instituto de Matemática MultidisciplinarUniversitat Politècnica de ValènciaValenciaSpain
  2. 2.Department of MathematicsHamedan Branch, Islamic Azad UniversityHamedanIran

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