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Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior

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Abstract

In this paper, we present a family of optimal, in the sense of Kung–Traub’s conjecture, iterative methods for solving nonlinear equations with eighth-order convergence. Our methods are based on Chun’s fourth-order method. We use the Ostrowski’s efficiency index and several numerical tests in order to compare the new methods with other known eighth-order ones. We also extend this comparison to the dynamical study of the different methods.

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Acknowledgments

The authors would like to thank Mr. Francisco Chicharro for his valuable help for drawing the dynamical planes and to the anonymous referees, whose suggestions have improved the readability of this paper.

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Authors and Affiliations

  1. Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain

    A. Cordero & J. R. Torregrosa

  2. Department of Mathematics, Islamic Azad University, Najafabad Branch, Najafabad, Iran

    M. Fardi

  3. Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, Iran

    M. Ghasemi

Authors
  1. A. Cordero
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  2. M. Fardi
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  3. M. Ghasemi
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  4. J. R. Torregrosa
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Corresponding author

Correspondence to A. Cordero.

Additional information

This research was supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-02 and by the Center of Excellence for Mathematics, University of Shahrekord, Iran.

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Cordero, A., Fardi, M., Ghasemi, M. et al. Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior. Calcolo 51, 17–30 (2014). https://doi.org/10.1007/s10092-012-0073-1

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  • DOI: https://doi.org/10.1007/s10092-012-0073-1

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