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Improving the Dynamics of Steffensen-type Methods
(Applied Mathematics and Information Sciences, 2015)
The dynamics of Steffesen-type methods, using a graphical tool for showing the basins of attraction, is presented. The
study includes as particular cases, Steffesen-type modifications of the Newton, the two-steps, the ...
A new fourth-order family for solving nonlinear problems and its dynamics
(Journal of Mathematical Chemistry, 2015-03)
In this manuscript, a new parametric class of iterative methods for solving nonlinear systems of equations is proposed. Its fourth-order of convergence is proved and a dynamical analysis on low-degree polynomials is made ...
Stability analysis of a parametric family of iterative methods for solving nonlinear models
(Applied Mathematics and Computation, 2016-07)
A one-parametric family of fourth-order iterative methods for solving nonlinear systems is presented, proving the fourth-order of convergence of all members in this family, except one of them whose order is five. The methods ...
On the convergence of an optimal fourth-order family of methods and its dynamics
(Applied Mathematics and Computation, 2015-02)
In this paper, we present the study of the semilocal and local convergence of an optimal fourth-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials ...
On the election of the damped parameter of a two-step relaxed Newton-type method
(Nonlineard Dynamics, 2016-04)
In this paper, we are interested to justified two typical hypotheses that appear in the convergence analysis, |λ|≤2|λ|≤2 and z0z0 sufficient close to z∗z∗ . In order to proof these ideas, the dynamics of a damped ...
On the convergence of a higher order family of methods and its dynamics
(Journal of Computational and Applied Mathematics, 2017-01)
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 ...
Introduction to complex dynamics
(Contemporary study of iterative methods: convergence, dynamics and applications, 2018)
In this chapter some dynamical concepts of complex dynamics that will be used in this book are presented. Moreover, some graphics illustrating the theoretical concepts are shown in order to let the reader understand them better.
A complex dynamical approach of Chebyshev’s method
(SeMA Journal, 2015-11)
The aim of this paper is to investigate the iterative root-finding Chebyshev’s method from a dynamical perspective. We analyze the behavior of the method applied to low degree polynomials. In this work we focus on the ...