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An efficient two-parametric family with memory for nonlinear equations

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Abstract

A new two-parametric family of derivative-free iterative methods for solving nonlinear equations is presented. First, a new biparametric family without memory of optimal order four is proposed. The improvement of the convergence rate of this family is obtained by using two self-accelerating parameters. These varying parameters are calculated in each iterative step employing only information from the current and the previous iteration. The corresponding R-order is 7 and the efficiency index 71/3 = 1.913. Numerical examples and comparison with some existing derivative-free optimal eighth-order schemes are included to confirm the theoretical results. In addition, the dynamical behavior of the designed method is analyzed and shows the stability of the scheme.

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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

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

    Parisa Bakhtiari

Authors
  1. Alicia Cordero
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  2. Taher Lotfi
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  3. Parisa Bakhtiari
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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., Bakhtiari, P. et al. An efficient two-parametric family with memory for nonlinear equations. Numer Algor 68, 323–335 (2015). https://doi.org/10.1007/s11075-014-9846-8

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  • DOI: https://doi.org/10.1007/s11075-014-9846-8

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