Listar por tema "nonlinear equations"
Mostrando ítems 1-12 de 12
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A complex dynamical approach of Chebyshev’s method
(SeMA Journal, 11/2015)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 ... -
A first overview on the real dynamics of Chebyshev's method
(Journal of Computational and Applied Mathematics, 07/2017)In this paper we explore some properties of the well known root-finding Chebyshev’s method applied to polynomials defined on the real field. In particular we are interested in showing the existence of extraneous fixed ... -
A new tool to study real dynamics: The convergence plane
(Applied Mathematics and Computation, 12/2014)In this paper, the author presents a graphical tool that allows to study the real dynamics of iterative methods whose iterations depends on one parameter in an easy and compact way. This tool gives the information as ... -
Design and Complex Dynamics of Potra–Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications
(MDPIMathematics, 11/10/2019)In this paper, using the idea of weight functions on the Potra–Pták method, an optimal fourth order method, a non optimal sixth order method, and a family of optimal eighth order methods are proposed. These methods are ... -
Generating Root-Finder Iterative Methods of Second Order: Convergence and Stability
(Axioms, 06/05/2019)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 ... -
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 ... -
Inexact two-point Newton-like methods
(Elsevier, 2018)In this chapter the applicability of inexact two-point Newton-like method for solving nonlinear equations is extended. Moreover, we present some numerical examples validating the theoretical results. -
Iterative schemes for finding all roots simultaneously of nonlinear equations
(Applied Mathematics Letters, 2022)In this paper, we propose a procedure that can be added to any iterative scheme in order to turn it into an iterative method for approximating all roots simultaneously of any nonlinear equations. By applying this procedure ... -
Memory in the iterative processes for nonlinear problems
(Mathematical Methods in the Applied Sciences, 2023)In this paper, we study different ways for introducing memory to a parametric family of optimal two-step iterative methods. We study the convergence and the stability, by means of real dynamics, of the methods obtained by ... -
Second derivative free sixth order continuation method for solving nonlinear equations with applications
(Journal of Mathematical Chemistry, 08/2018)In this paper, we deal with the study of convergence analysis of modified parameter based family of second derivative free continuation method for solving nonlinear equations. We obtain the order of convergence is at least ... -
Stability study of eighth-order iterative methods for solving nonlinear equations
(Journal of Computational and Applied Mathematics, 01/2016)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, 01/2017)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 ...
