Artidiello Moreno, Santiago de Jesús; Chicharro López, Francisco Israel; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Taylor & Francis Ltd, 2013-10)
In this paper, a family of new fourth-order optimal iterative methods for solving nonlinear equations is proposed. The classical King s family of fourth-order schemes is obtained as an special case. We also present results ...
Cevallos Alarcón, Fabricio Alfredo(Universitat Politècnica de València, 2023-05-22)
[ES] La resolución de ecuaciones y sistemas no lineales es un tema de gran interés teórico-práctico, pues muchos modelos matemáticos de la ciencia o de la industria se expresan mediante sistemas no lineales o ecuaciones ...
[EN] In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order ...
Cordero Barbero, Alicia; Franqués García, Antonio María; Torregrosa Sánchez, Juan Ramón(Springer, 2015-07-11)
[EN] In this paper, a parametric family of iterative methods for solving nonlinear systems, including Homeier’s scheme is presented, proving its third-order of convergence. The numerical section is devoted to obtain an ...
[EN] In this work, we introduce a modification into the technique, presented in A. Cordero, J.L. Hueso, E. Martinez, and J.R. Torregrosa [Increasing the convergence order of an iterative method for nonlinear systems, Appl. ...
[EN] In this paper, a two-step class of fourth-order iterative methods for solving systems of nonlinear equations is presented. We further extend the two-step class to establish a new sixth-order family which requires only ...
Behl, Ramandeep; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Alshomrani, Ali Saleh(MDPI AG, 2018)
[EN] In this manuscript, a new type of study regarding the iterative methods for solving nonlinear models is presented. The goal of this work is to design a new fourth-order optimal family of two-step iterative schemes, ...
[EN] This paper is devoted to the construction and analysis of an efficient k-step iterative method for nonlinear equations. The main advantage of this method is that it does not need to evaluate any high order Frechet ...
Amat, Sergio; Argyros, Ioannis K.; Busquier Saez, Sonia; Hernández-Verón, Miguel Angel; Martínez Molada, Eulalia(Elsevier, 2018-12-01)
[EN] This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. The methods have high order of convergence but only using first order ...
Hernandez Verón, Miguel Angel; Martínez Molada, Eulalia(Springer Verlag (Germany), 2015-10)
[EN] In this paper the semilocal convergence for an alternative to the three steps Newton's method with frozen derivative is presented. We analyze the generalization of convergence conditions given by w-conditioned ...
Cordero Barbero, Alicia; Jordan-Lluch, Cristina; Torregrosa Sánchez, Juan Ramón(Elsevier, 2015-02)
In this paper, a unified point of view that includes the most of one-point Newton-type iterative
methods for solving nonlinear equations is introduced. A simple idea to design iterative
methods with quadratic or cubic ...
[EN] It is well known that the optimal iterative methods are of more significance than the non-optimal ones in view of their efficiency and convergence speed. There are only a few number of optimal iterative methods for ...
[EN] In this paper, a new technique to construct a family of divided differences for designing derivative-free iterative methods for solving nonlinear systems is proposed. By using these divided differences any kind of ...
Capdevila Brown, Raudys Rafael(Universitat Politècnica de València, 2024-01-03)
[ES] Se puede afirmar que la inmensa mayoría de los fenómenos de la naturaleza estudiados tienen un carácter no lineal.
Muchos de estos problemas se pueden modelar utilizando ecuaciones diferenciales no lineales (EDNL) ...
Hernández-Verón, Miguel Angel; Martínez Molada, Eulalia; Teruel-Ferragud, Carles(Springer-Verlag, 2017)
[EN] In this paper, we analyze the semilocal convergence of k-steps Newton's method with frozen first derivative in Banach spaces. The method reaches order of convergence k + 1. By imposing only the assumption that the ...
[EN] In this work we focus on location and approximation of a solution of nonlinear integral equations of Hammerstein-type when the kernel is non-separable through a high order iterative process. For this purpose, we ...
Amiri, A. R.; Cordero Barbero, Alicia; Darvishi, M. T.; Torregrosa Sánchez, Juan Ramón(Springer-Verlag, 2019-05)
[EN] The dynamical properties of a family of forward, central divided differences and Richardson extrapolation technique are studied. Applying these tools, an iterative method for solving nonlinear systems can be transformed ...
Babajee, D.K.R.; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2016)
[EN] Many iterative methods for solving nonlinear equations have been developed recently. The main advantage claimed by their authors is the improvement of the order of convergence. In this work, we compare their dynamical ...