Complex dynamics of derivative-free methods for nonlinear equations

  1. Chicharro, Francisco. 1
  2. Cordero, A. 1
  3. Gutiérrez, J.M. 2
  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

Journal:
Applied Mathematics and Computation

ISSN: 0096-3003

Year of publication: 2013

Volume: 219

Issue: 12

Pages: 7023-7035

Type: Article

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DOI: 10.1016/J.AMC.2012.12.075 SCOPUS: 2-s2.0-84874024608 WoS: WOS:000315708700062 GOOGLE SCHOLAR

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Abstract

The dynamical behavior of two iterative derivative-free schemes, Steffensen and M4 methods, is studied in case of quadratic and cubic polynomials. The parameter plane is analyzed for both procedures on quadratic polynomials. Different dynamical planes are showed when the mentioned methods are applied on particular cubic polynomials with real or complex coefficients. The property of immersion of the basins of attraction in all cases is analyzed. © 2013 Elsevier Inc. All rights reserved.