Journal of Mathematical Chemistry

, Volume 56, Issue 7, pp 2117–2131

Ball convergence of a sixth-order Newton-like method based on means under weak conditions

• Á. A. Magreñán
• I. K. Argyros
• J. J. Rainer
• J. A. Sicilia
Original Paper

Abstract

We study the local convergence of a Newton-like method of convergence order six to approximate a locally unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the seventh derivative or even higher. The convergence in this study is shown under hypotheses on the first derivative although only the first derivative appears in these methods. Hence, the applicability of the method is expanded. Finally, we solve the problem of the fractional conversion in the ammonia process showing the applicability of the theoretical results.

Keywords

Newton-like method Local convergence Stolarky means Gini means Efficiency index

Mathematics Subject Classification

65D10 65D99 65G99 90C30

Notes

Acknowledgements

The research of this author was supported by Universidad Internacional de La Rioja (UNIR, http://www.unir.net), under the Plan Propio de Investigación, Desarrollo e Innovación 4 [2017–2019]. Research group: Modelación matemática aplicada a la ingeniería(MOMAIN), by Programa de Apoyo a la investigación de la fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 19374/PI714 and by Ministerio de Ciencia y Tecnología MTM2014-52016-C2-01-P.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

• Á. A. Magreñán
• 1
• I. K. Argyros
• 2
• J. J. Rainer
• 1
Email author
• J. A. Sicilia
• 1
1. 1.Escuela de IngenieríaUniversidad Internacional de La RiojaLogroñoSpain
2. 2.Department of Mathematics SciencesCameron UniversityLawtonUSA