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Open AccessArticle

Study of Local Convergence and Dynamics of a King-Like Two-Step Method with Applications

1
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
2
Departamento de Matemáticas y Computación, Universidad de La Rioja, Madre de Dios 53, 26006 Logroño (La Rioja), Spain
3
Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Avenida de la Paz 123, 26006 Logroño (La Rioja), Spain
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(7), 1062; https://doi.org/10.3390/math8071062
Received: 9 May 2020 / Revised: 29 May 2020 / Accepted: 4 June 2020 / Published: 1 July 2020
In this paper, we present the local results of the convergence of the two-step King-like method to approximate the solution of nonlinear equations. In this study, we only apply conditions to the first derivative, because we only need this condition to guarantee convergence. As a result, the applicability of the method is expanded. We also use different convergence planes to show family behavior. Finally, the new results are used to solve some applications related to chemistry. View Full-Text
Keywords: king-like iterative methods; local convergence; lipschitz conditions; dynamics king-like iterative methods; local convergence; lipschitz conditions; dynamics
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MDPI and ACS Style

Argyros, I.K.; Magreñán, Á.A.; Moysi, A.; Sarría, Í.; Sicilia Montalvo, J.A. Study of Local Convergence and Dynamics of a King-Like Two-Step Method with Applications. Mathematics 2020, 8, 1062.

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