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On improved three-step schemes with high efficiency index and their dynamics

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Abstract

This paper presents an improvement of the sixth-order method of Chun and Neta as a class of three-step iterations with optimal efficiency index, in the sense of Kung-Traub conjecture. Each member of the presented class reaches the highest possible order using four functional evaluations. Error analysis will be studied and numerical examples are also made to support the theoretical results. We then present results which describe the dynamics of the presented optimal methods for complex polynomials. The basins of attraction of the existing optimal methods and our methods are presented and compared to illustrate their performances.

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Authors and Affiliations

  1. Scientific & Academic Research Council, African Network for Policy Research & Advocacy for Sustainability, Mauritius, Mauritius

    Diyashvir K. R. Babajee

  2. IEEE Subsection, Mauritius, Mauritius

    Diyashvir K. R. Babajee

  3. Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022, Valencia, Spain

    Alicia Cordero & Juan R. Torregrosa

  4. Department of Mathematics, Islamic Azad University, Zahedan Branch, PO Box 987-98138, Zahedan, Iran

    Fazlollah Soleymani

Authors
  1. Diyashvir K. R. Babajee
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  2. Alicia Cordero
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  3. Fazlollah Soleymani
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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 and FONDOCYT República Dominicana.

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Babajee, D.K.R., Cordero, A., Soleymani, F. et al. On improved three-step schemes with high efficiency index and their dynamics. Numer Algor 65, 153–169 (2014). https://doi.org/10.1007/s11075-013-9699-6

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  • DOI: https://doi.org/10.1007/s11075-013-9699-6

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