On the Efficiency of a Family of Steffensen-Like Methods with Frozen Divided Differences

  1. Amat, S. 1
  2. Busquier, S. 1
  3. Grau-Sánchez, M. 2
  4. Hernández-Verón, M.A. 3
  1. 1 Universidad Politécnica de Cartagena
    info

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

  2. 2 Universitat Politècnica de Catalunya
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    Universitat Politècnica de Catalunya

    Barcelona, España

    ROR https://ror.org/03mb6wj31

  3. 3 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

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Revista:
Computational Methods in Applied Mathematics

ISSN: 1609-4840

Año de publicación: 2017

Volumen: 17

Número: 2

Páginas: 187-199

Tipo: Artículo

DOI: 10.1515/CMAM-2016-0039 SCOPUS: 2-s2.0-85016803504 WoS: WOS:000397674800001 GOOGLE SCHOLAR

Otras publicaciones en: Computational Methods in Applied Mathematics

Resumen

A generalized k-step iterative method from Steffensen's method with frozen divided difference operator for solving a system of nonlinear equations is studied and the maximum computational efficiency is computed. Moreover, a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the method and the computational efficiency are both well deduced. By using a technique based on recurrence relations, the semilocal convergence of the family is studied. Finally, some numerical experiments related to the approximation of nonlinear elliptic equations are reported. A comparison with other derivative-free families of iterative methods is carried out. © 2017 by De Gruyter.