A study on the local convergence and the dynamics of Chebyshev–Halley–type methods free from second derivative
Argyros, Ioannis K
Magreñán, Á. Alberto (UNIR)
Tipo de Ítem:Articulo Revista Indexada
We study the local convergence of Chebyshev-Halley-type methods of convergence order at least five to approximate a locally unique solution of a nonlinear equation. Earlier studies such as Behl (2013), Bruns and Bailey (Chem. Eng. Sci 32, 257–264, 1977), Candela and Marquina (Computing 44, 169–184, 1990), (Computing 45(4):355–367, 1990), Chicharro et al. (2013), Chun (Appl. Math. Comput, 190(2):1432–1437, 1990), Cordero et al. (Appl.Math. Lett. 26, 842–848, 2013), Cordero et al. (Appl. Math. Comput. 219, 8568–8583, 2013), Cordero and Torregrosa (Appl. Math. Comput. 190, 686–698, 2007), Ezquerro and Hernández (Appl. Math. Optim. 41(2):227–236, 2000), (BIT Numer. Math. 49, 325–342, 2009), (J. Math. Anal. Appl. 303, 591–601, 2005), Gutiérrez and Hernández (Comput. Math. Applic. 36(7):1–8, 1998), Ganesh and Joshi (IMA J. Numer. Anal. 11, 21–31, 1991), Hernández (Comput. Math. Applic. 41(3–4):433–455, 2001), Hernández and Salanova (Southwest J. Pure Appl. Math. 1, 29–40, 1999), Jarratt (Math. Comput. 20(95):434–437, 1996), Kou and Li (Appl. Math. Comput. 189, 1816–1821, 2007), Li (Appl. Math. Comput. 235, 221–225, 2014), Ren et al. (Numer. Algorithm. 52(4):585–603, 2009), Wang et al. (Numer. Algorithm. 57, 441–456, 2011), Kou et al. (Numer. Algorithm. 60, 369–390, 2012) show convergence under hypotheses on the third derivative or even higher. The convergence in this study is shown under hypotheses on the first derivative. Hence, the applicability of the method is expanded. The dynamical analyses of these methods are also studied. Finally, numerical examples are also provided to show that our results apply 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 ...