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Mathematics 2019, 7(3), 225; https://doi.org/10.3390/math7030225

Study of a High Order Family: Local Convergence and Dynamics

1
Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain
2
Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
3
Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain
4
Facultad de Educación, Universidad Internacional de La Rioja, 26006 Logroño, Spain
*
Author to whom correspondence should be addressed.
Received: 10 December 2018 / Revised: 22 February 2019 / Accepted: 25 February 2019 / Published: 28 February 2019
(This article belongs to the Special Issue Iterative Methods for Solving Nonlinear Equations and Systems)
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Abstract

The study of the dynamics and the analysis of local convergence of an iterative method, when approximating a locally unique solution of a nonlinear equation, is presented in this article. We obtain convergence using a center-Lipschitz condition where the ball radii are greater than previous studies. We investigate the dynamics of the method. To validate the theoretical results obtained, a real-world application related to chemistry is provided. View Full-Text
Keywords: high order; sixteenth order convergence method; local convergence; dynamics high order; sixteenth order convergence method; local convergence; dynamics
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Amorós, C.; Argyros, I.K.; González, R.; Magreñán, Á.A.; Orcos, L.; Sarría, Í. Study of a High Order Family: Local Convergence and Dynamics. Mathematics 2019, 7, 225.

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