Stability analysis of a parametric family of iterative methods for solving nonlinear models

  1. Cordero, A. 1
  2. Gutiérrez, J.M. 2
  3. Magreñán, Á.A. 3
  4. Torregrosa, J.R. 1
  1. 1 Universidad Politécnica de Valencia
    info

    Universidad Politécnica de Valencia

    Valencia, España

    ROR https://ror.org/01460j859

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  3. 3 Universidad Internacional de La Rioja
    info

    Universidad Internacional de La Rioja

    Logroño, España

    ROR https://ror.org/029gnnp81

Revista:
Applied Mathematics and Computation

ISSN: 0096-3003

Ano de publicación: 2016

Volume: 285

Páxinas: 26-40

Tipo: Artigo

DOI: 10.1016/J.AMC.2016.03.021 SCOPUS: 2-s2.0-84962858062 WoS: WOS:000375403400003 GOOGLE SCHOLAR

Outras publicacións en: Applied Mathematics and Computation

Resumo

A one-parametric family of fourth-order iterative methods for solving nonlinear systems is presented, proving the fourth-order of convergence of all members in this family, except one of them whose order is five. The methods in our family are numerically compared with other known methods in terms of the classical efficiency index (order of convergence and number of functional evaluations) and in terms of the operational efficiency index, which also takes into account the total number of product-quotients per iteration. In order to analyze its stability and its dynamical properties, the parameter space for quadratic polynomials is shown. The stability of the strange fixed points is studied in this case. We note that even for this particular case, the family presents a very interesting dynamical behavior. The analysis of the parameter plane allows us to find values for the involved parameter with good stability properties as well as other values with bad numerical behavior. Finally, amongst the first ones, there is a special value of the parameter related to a fifth-order method in the family. © 2016 Elsevier Inc. All rights reserved.