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A stable class of improved second-derivative free Chebyshev-Halley type methods with optimal eighth order convergence

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Abstract

In this paper, we present a uniparametric family of modified Chebyshev-Halley type methods with optimal eighth-order of convergence. In terms of computational cost, each member of the family requires only four functional evaluations per step, and hence is optimal in the sense of Kung-Traub conjecture. Moreover, in order to have additional information to choose some elements of the class, in particular some stable enough, we use complex dynamics tools to analyze their stability. Then, some ranges of values of the parameter are found to be avoided but we show that the region of stable members of this family is vast. It is found by way of illustration that these proposed methods are very useful in high precision computations.

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Authors and Affiliations

  1. Multidisciplinary Institute of Mathematics, Universitat Politècnica de València, 46022, Valencia, Spain

    Alicia Cordero & Juan R. Torregrosa

  2. University Institute of Engineering and Technology, Panjab University, 160 014, Chandigarh, India

    Munish Kansal & Vinay Kanwar

Authors
  1. Alicia Cordero
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  2. Munish Kansal
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  3. Vinay Kanwar
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  4. Juan R. Torregrosa
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Corresponding author

Correspondence to Alicia Cordero.

Additional information

This research was partially supported by Ministerio de Economía y Competitividad MTM2014-52016-C2-2-P.

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Cordero, A., Kansal, M., Kanwar, V. et al. A stable class of improved second-derivative free Chebyshev-Halley type methods with optimal eighth order convergence. Numer Algor 72, 937–958 (2016). https://doi.org/10.1007/s11075-015-0075-6

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  • DOI: https://doi.org/10.1007/s11075-015-0075-6

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