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    Optimal Fourth-Order Weerakoon–Fernando-Type Methods for Multiple Roots and Their Dynamics

    Autor: 
    Chand, Prem Bahadur
    ;
    Chicharro, Francisco Israel (1)
    ;
    Jain, Pankaj
    ;
    Sethi, Kriti
    Fecha: 
    16/04/2019
    Palabra clave: 
    Non-linear equations; Newton-type method; multiple root; complex dynamics; fixed and critical points; basin of attraction; JCR; Scopus
    Tipo de Ítem: 
    article
    URI: 
    https://reunir.unir.net/handle/123456789/8283
    DOI: 
    https://doi.org/10.1007/s00009-019-1350-x
    Dirección web: 
    https://link.springer.com/article/10.1007%2Fs00009-019-1350-x
    Resumen:
    In this paper, we present optimal fourth-order methods for finding multiple roots of non-linear equations, where the multiplicity is known in advance. These methods are based on the third-order method given by Weerakoon and Fernando for simple roots. The dynamical behavior of these methods around multiple roots is studied using basin of attraction in complex plane. We also present numerical examples to confirm our theoretical results.
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