An optimal three-point eighth-order iterative method without memory for solving nonlinear equations with its dynamics

  1. Matthies, G. 1
  2. Salimi, M. 13
  3. Sharifi, S. 4
  4. Varona, J.L. 2
  1. 1 Dresden University of Technology
    info

    Dresden University of Technology

    Dresde, Alemania

    ROR https://ror.org/042aqky30

  2. 2 Universidad de La Rioja
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    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  3. 3 Universiti Putra Malaysia
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    Universiti Putra Malaysia

    Seri Kembangan, Malasia

    ROR https://ror.org/02e91jd64

  4. 4 Università per stranieri Dante Alighieri
    info

    Università per stranieri Dante Alighieri

    Regio de Calabria, Italia

    ROR https://ror.org/01gz5zx42

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Revista:
Japan Journal of Industrial and Applied Mathematics

ISSN: 0916-7005

Año de publicación: 2016

Volumen: 33

Número: 3

Páginas: 751-766

Tipo: Artículo

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DOI: 10.1007/S13160-016-0229-5 SCOPUS: 2-s2.0-84994403977 WoS: WOS:000389894100013 GOOGLE SCHOLAR

Otras publicaciones en: Japan Journal of Industrial and Applied Mathematics

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Proyectos relacionados

Ortogonalidad, teoría de la aproximación y aplicaciones en física matemática.

2016/00008/001

Resumen

We present a three-point iterative method without memory for solving nonlinear equations in one variable. The proposed method provides convergence order eight with four function evaluations per iteration. Hence, it possesses a very high computational efficiency and supports Kung–Traub’s conjecture. The construction, the convergence analysis, and the numerical implementation of the method will be presented. Using several test problems, the proposed method will be compared with existing methods of convergence order eight concerning accuracy and basins of attraction. Furthermore, some measures are used to judge methods with respect to their performance in finding the basins of attraction. © 2016 The JJIAM Publishing Committee and Springer Japan