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

Ioannis K. Argyros, Ángel Alberto Magreñán, Alejandro Moysi, Íñigo Sarría and Juan Antonio Sicilia Montalvo
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Ioannis K. Argyros: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Ángel Alberto Magreñán: Departamento de Matemáticas y Computación, Universidad de La Rioja, Madre de Dios 53, 26006 Logroño (La Rioja), Spain
Alejandro Moysi: Departamento de Matemáticas y Computación, Universidad de La Rioja, Madre de Dios 53, 26006 Logroño (La Rioja), Spain
Íñigo Sarría: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Avenida de la Paz 123, 26006 Logroño (La Rioja), Spain
Juan Antonio Sicilia Montalvo: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Avenida de la Paz 123, 26006 Logroño (La Rioja), Spain

Mathematics, 2020, vol. 8, issue 7, 1-12

Abstract: 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.

Keywords: king-like iterative methods; local convergence; lipschitz conditions; dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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