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Open AccessArticle

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

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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