On the local convergence and the dynamics of Chebyshev–Halley methods with six and eight order of convergence
Magreñán, Á. Alberto (UNIR)
Argyros, Ioannis K
Tipo de Ítem:Articulo Revista Indexada
We study the local convergence of Chebyshev–Halley methods with six and eight order of convergence to approximate a locally unique solution of a nonlinear equation. In Sharma (2015) (see Theorem 1, p. 121) the convergence of the method was shown under hypotheses reaching up to the third derivative. The convergence in this study is shown under hypotheses on the first derivative. Hence, the applicability of the method is expanded. The dynamics of these methods are also studied. Finally, numerical examples examining dynamical planes are also provided in this study to solve equations in cases where earlier studies cannot apply.
Este ítem aparece en la(s) siguiente(s) colección(es)
Mostrando ítems relacionados por Título, autor o materia.
Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation Argyros, Ioannis K; Magreñán, Á. Alberto (UNIR); Orcos, Lara (UNIR) (Journal of Mathematical Chemistry, 08/2016)We present a local convergence analysis of a derivative free fourth order method with one parameter based on rational interpolation in order to approximate a locally unique root of a function. The method is optimal in the ...
Local convergence and the dynamics of a two-point four parameter Jarratt-like method under weak conditions Amat, S (UNIR); Argyros, Ioannis K; Busquier, S; Magreñán, Á. Alberto (UNIR) (Numerical Algorithms, 02/2017)We present a local convergence analysis of a two-point four parameter Jarratt-like method of high convergence order in order to approximate a locally unique solution of a nonlinear equation. In contrast to earlier studies ...
Argyros, Ioannis K; Cordero, Alicia; Magreñán, Á. Alberto (UNIR); Torregrosa, Juan Ramón (Journal of Computational and Applied Mathematics, 01/2017)In this paper, we present the study of the local convergence of a higher-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials is studied. Some ...