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    Convergence and Dynamics of a Higher-Order Method

    Autor: 
    Moysi, Alejandro
    ;
    Argyros, Ioannis K
    ;
    Regmi, Samundra
    ;
    González, Daniel
    ;
    Magreñán, Á. Alberto
    ;
    Sicilia, Juan Antonio
    Fecha: 
    03/2020
    Palabra clave: 
    high-order iterative method; convergence; dynamics; Scopus; JCR
    Revista / editorial: 
    Symmetry
    Citación: 
    Moysi, A.; Argyros, I.K.; Regmi, S.; González, D.; Magreñán, Á.A.; Sicilia, J.A. Convergence and Dynamics of a Higher-Order Method. Symmetry 2020, 12, 420.
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/10329
    DOI: 
    https://doi.org/10.3390/sym12030420
    Dirección web: 
    https://www.mdpi.com/2073-8994/12/3/420
    Open Access
    Resumen:
    Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves some iterative method generating a sequence approximating the solution. That is why, in this work, we analyze the convergence in a local form for an iterative method with a high order to find the solution of a nonlinear equation. We extend the applicability of previous results using only the first derivative that actually appears in the method. This is in contrast to either works using a derivative higher than one, or ones not in this method. Moreover, we consider the dynamics of some members of the family in order to see the existing differences between them.
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