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Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability
In this paper, a simple family of one-point iterative schemes for approximating the solutions of nonlinear equations, by using the procedure of weight functions, is derived. The convergence analysis is presented, showing ...
Anomalies in the convergence of Traub‐type methods with memory
The stability analysis of a new family of iterative methods with memory isintroduced. This family, designed from Traub's method, allows to add memorythrough the introduction of an accelerating parameter. Hence, the speed ...
On the effect of the multidimensional weight functions on the stability of iterative processes
In this work, we start from a family of iterative methods for solving nonlinear multidimensional problems, designed using the inclusion of a weight function on its iterative expression. A deep dynamical study of the family ...
Anomalies in the convergence of Traub-type methods with memory
The stability analysis of a new family of iterative methods with memory is introduced. This family, designed from Traub's method, allows to add memory through the introduction of an accelerating parameter. Hence, the speed ...
Stability study of eighth-order iterative methods for solving nonlinear equations
In this paper, we study the stability of the rational function associated to a known family of eighth-order iterative schemes on quadratic polynomials. The asymptotic behavior of the fixed points corresponding to the ...
Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane
The real dynamics of a family of fourth-order iterative methods is studied when it is applied on quadratic polynomials. A Scaling Theorem is obtained and the conjugacy classes are analyzed. The convergence plane is used ...
A new fourth-order family for solving nonlinear problems and its dynamics
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 ...
Global analysis of the dynamics of a mathematical model to intermittent HIV treatment
(Springer, 2020-07-09)
The aim of this paper is to study the qualitative dynamics of a piecewise smooth system modeling the intermittent treatment of the human immunodeficiency virus. Typical singularities and closed orbits are observable, and ...
Introduction to complex dynamics
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.
Measures of the Basins of Attracting n-Cycles for the Relaxed Newton's Method
The relaxed Newton's method modifies the classical Newton's method with a parameter h in such a way that when it is applied to a polynomial with multiple roots and we take as parameter one of these multiplicities, it is ...