Study of a High Order Family: Local Convergence and Dynamics

Cristina Amorós, Ioannis K. Argyros, Ruben González, Á. Alberto Magreñán, Lara Orcos and Íñigo Sarría
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Cristina Amorós: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain
Ioannis K. Argyros: Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
Ruben González: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain
Á. Alberto Magreñán: Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004 Logroño, Spain
Lara Orcos: Facultad de Educación, Universidad Internacional de La Rioja, 26006 Logroño, Spain
Íñigo Sarría: Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain

Mathematics, 2019, vol. 7, issue 3, 1-14

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.

Keywords: high order; sixteenth order convergence method; local convergence; dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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