Listar por tema "complex dynamics"
Mostrando ítems 1-8 de 8
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A new fourth-order family for solving nonlinear problems and its dynamics
(Journal of Mathematical Chemistry, 03/2015)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 ... -
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 ... -
On the convergence of a higher order family of methods and its dynamics
(Journal of Computational and Applied Mathematics, 01/2017)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 ... -
On the convergence of an optimal fourth-order family of methods and its dynamics
(Applied Mathematics and Computation, 02/2015)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, 04/2016)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 ... -
Optimal Fourth-Order Weerakoon–Fernando-Type Methods for Multiple Roots and Their Dynamics
(Mediterranean Journal of Mathematics, 16/04/2019)In this paper, we present optimal fourth-order methods for finding multiple roots of non-linear equations, where the multiplicity is known in advance. These methods are based on the third-order method given by Weerakoon ... -
Stability analysis of a parametric family of iterative methods for solving nonlinear models
(Applied Mathematics and Computation, 07/2016)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 and applicability of iterative methods with memory
(Journal of Mathematical Chemistry, 15/03/2019)Based on the third-order Traub’s method, two iterative schemes with memory are introduced. The proper inclusion of accelerating parameters allows the introduction of memory. Therefore, the order of convergence of the ...