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    Study of local convergence and dynamics of a king-like two-step method with applications

    Autor: 
    Argyros, Ioannis K
    ;
    Magreñán, Á. Alberto
    ;
    Moysi, Alejandro
    ;
    Sarría, Íñigo (1)
    ;
    Sicilia, Juan Antonio (1)
    Fecha: 
    01/07/2020
    Palabra clave: 
    king-like iterative methods; local convergence; lipschitz conditions; dynamics; Scopus; JCR
    Tipo de Ítem: 
    Articulo Revista Indexada
    URI: 
    https://reunir.unir.net/handle/123456789/10612
    DOI: 
    https://doi.org/10.3390/math8071062
    Dirección web: 
    https://www.mdpi.com/2227-7390/8/7/1062
    Open Access
    Resumen:
    In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because we only need this condition to guarantee convergence. As a result, the applicability of the method is expanded. We also use different convergence planes to show family behavior. Finally, the new results are used to solve some applications related to chemistry.
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