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Widening basins of attraction of optimal iterative methods

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Abstract

In this work, we analyze the dynamical behavior on quadratic polynomials of a class of derivative-free optimal parametric iterative methods, designed by Khattri and Steihaug. By using their parameter as an accelerator, we develop different methods with memory of orders three, six and twelve, without adding new functional evaluations. Then a dynamical approach is made, comparing each of the proposed methods with the original ones without memory, with the following empiric conclusion: Basins of attraction of iterative schemes with memory are wider and the behavior is more stable. This has been numerically checked by estimating the solution of a practical problem, as the friction factor of a pipe and also of other nonlinear academic problems.

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Acknowledgments

The authors thank to the anonymous referees for their valuable comments and for the suggestions that have improved the final version of the paper.

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Authors and Affiliations

  1. Young Researchers and Elite Club, Hamedan Branch, Islamic Azad University, Hamedan, Iran

    Parisa Bakhtiari

  2. Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain

    Alicia Cordero & Juan R. Torregrosa

  3. Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

    Taher Lotfi & Kathayoun Mahdiani

Authors
  1. Parisa Bakhtiari
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  2. Alicia Cordero
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  3. Taher Lotfi
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  4. Kathayoun Mahdiani
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  5. Juan R. Torregrosa
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Corresponding author

Correspondence to Juan R. Torregrosa.

Additional information

This research was supported by Islamic Azad University, Hamedan Branch, Ministerio de Economía y Competitividad MTM2014-52016-C02-2-P and Generalitat Valenciana PROMETEO/2016/089.

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Bakhtiari, P., Cordero, A., Lotfi, T. et al. Widening basins of attraction of optimal iterative methods. Nonlinear Dyn 87, 913–938 (2017). https://doi.org/10.1007/s11071-016-3089-2

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  • DOI: https://doi.org/10.1007/s11071-016-3089-2

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