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Two Optimal General Classes of Iterative Methods with Eighth-Order

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Abstract

Two new three-step classes of optimal iterative methods to approximate simple roots of nonlinear equations, satisfying the Kung-Traub’s conjecture, are designed. The development of the methods and their convergence analysis are provided joint with a generalization of both processes. In order to check the goodness of the theoretical results, some concrete methods are extracted and numerical and dynamically compared with some known methods.

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Acknowledgements

The authors would like to render thanks to the reviewers for their comments and suggestions that have improved the readability of the paper.

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Authors and Affiliations

  1. Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022, Valencia, Spain

    Alicia Cordero & Juan R. Torregrosa

  2. Department of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

    Taher Lotfi & Katayoun Mahdiani

Authors
  1. Alicia Cordero
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  2. Taher Lotfi
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  3. Katayoun Mahdiani
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  4. Juan R. Torregrosa
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Corresponding author

Correspondence to Juan R. Torregrosa.

Additional information

This research was supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-02.

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Cordero, A., Lotfi, T., Mahdiani, K. et al. Two Optimal General Classes of Iterative Methods with Eighth-Order. Acta Appl Math 134, 61–74 (2014). https://doi.org/10.1007/s10440-014-9869-0

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  • DOI: https://doi.org/10.1007/s10440-014-9869-0

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