Dynamics of a fifth-order iterative method

  1. Gutiérrez, J.M. 2
  2. Plaza, S. 1
  3. Romero, N. 2
  1. 1 Universidad de Santiago de Chile
    info

    Universidad de Santiago de Chile

    Santiago de Chile, Chile

    ROR https://ror.org/02ma57s91

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
International Journal of Computer Mathematics

ISSN: 0020-7160

Año de publicación: 2012

Volumen: 89

Número: 6

Páginas: 822-835

Tipo: Artículo

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DOI: 10.1080/00207160.2012.663081 SCOPUS: 2-s2.0-84859199344 WoS: WOS:000301434500008 GOOGLE SCHOLAR

Otras publicaciones en: International Journal of Computer Mathematics

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Procesos iteratios para resolver ecuaciones no lineales: construcción, convergencia, eficacia, análisis dinámico y aplicaciones

2012/00014/001

Resumen

In this paper, we study the dynamical behaviour of a two-point iterative method with order of convergence five to solve nonlinear equations in the complex plane. In fact, we complement the dynamical study started in previous works with a more systematic analysis for polynomials with at most two different roots and different multiplicities. In addition, we characterize some polynomials of degree greater or equal to 4, such that the related methods are not generally convergent. We also analyse the degrees of the rational functions associated with two-point methods when they are applied to polynomials of degree n, showing their dependence on n2 and how this fact considerably complicates the dynamical study. © 2012 Copyright Taylor and Francis Group, LLC.