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On the local convergence of Kung-Traub’s two-point method and its dynamics

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Abstract

In this paper, the local convergence analysis of the family of Kung-Traub’s two-point method and the convergence ball for this family are obtained and the dynamical behavior on quadratic and cubic polynomials of the resulting family is studied. We use complex dynamic tools to analyze their stability and show that the region of stable members of this family is vast. Numerical examples are also presented in this study. This method is compared with several widely used solution methods by solving test problems from different chemical engineering application areas, e.g. Planck’s radiation law problem, natch distillation at infinite reflux, van der Waal’s equation, air gap between two parallel plates and flow in a smooth pipe, in order to check the applicability and effectiveness of our proposed methods.

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Acknowledgments

The authors would like to express their deep gratitude to the editors and referees for their valuable suggestions which led us to a better presentation of this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, College of Basic Sciences, Hamedan Branch, Islamic Azad University, Imam Khomeini Bldv, 6518115743, Hamedan, Iran

    Parandoosh Ataei Delshad & Taher Lotfi

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  1. Parandoosh Ataei Delshad
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  2. Taher Lotfi
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Correspondence to Taher Lotfi.

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Ataei Delshad, P., Lotfi, T. On the local convergence of Kung-Traub’s two-point method and its dynamics. Appl Math 65, 379–406 (2020). https://doi.org/10.21136/AM.2020.0322-18

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