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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 ...
Stability study of eighth-order iterative methods for solving nonlinear equations
(Journal of Computational and Applied Mathematics, 2016-01)
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 ...
Third-degree anomalies of Traub's method
(Journal of Computational and Applied Mathematics, 2017-01)
Traub’s method is a tough competitor of Newton’s scheme for solving nonlinear equations as well as nonlinear systems. Due to its third-order convergence and its low computational cost, it is a good procedure to be applied ...
Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane
(Mathematics and Computers in Simulation, 2014-11)
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 ...