Stability study of eighth-order iterative methods for solving nonlinear equations

Herramienta pedagógica basada en el desarrollo de una aplicación informática para la mejora del aprendizaje en matemática avanzada

“…Caracterización de las cuencas de atracción asociadas al método de Newton aplicado al polinomio (1) (izquierda) y (2) (derecha). Para proceder al estudio dinámico de este tipo de familias, lo primero que se hace es el estudio de los planos de parámetros (ver Gráfico 2) para determinar qué valores del parámetro van a tener un comportamiento dinámico que nos interese y cuáles no, con el fin de obtener una información más detallada de cada uno de los conceptos involucrados (Cordero, Magreñán, Quemada y Torregrosa 2016;Behl, Amat, Magreñán y Motsa, 2018; Magreñán, Argyros, Rainer y Sicilia, 2018).…”

Ball convergence theorems for Maheshwari-type eighth-order methods under weak conditions

“…These definitions have been used extensively [1,5,7] in order to avoid the computation of bounds involving higher order derivatives and still obtain the order of convergence (see also the three numerical examples where we compute ξ 1 ). 5.…”

“…Notice that the first two steps of method (1.2) constitute the fourth order method studied by Maheshwari in [6]. Other authors have also studied eight order methods [2,[8][9][10] or methods of order higher than 2 [1,[3][4][5][6][7]. Other single and multi-point methods can be found in [2,3,7,10] and the references there in.…”

Mathematical modeling and computational methods

“…In this context, I. Argyros et al [26] provide a semilocal as well as a local convergence analysis for Newton's and modified Newton's method, by using generalized Lipschitz continuity conditions. In [27], A. Cordero et al show the dynamical behavior of a family of eighth-order iterative schemes on quadratic polynomials. This study allows to choose some elements of the family with good stability properties.…”