Local convergence analysis of an eighth order scheme using hypothesis only on the first derivative
type: Item
instance of: scholarly article
title: Local convergence analysis of an eighth order scheme using hypothesis only on the first derivative
zbMATH Open document ID: 1461.65098
author: Xianqiang Yang
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: In this paper, we propose a local convergence analysis of an eighth order three-step method to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Further, we also study the dynamic behaviour of that scheme. In an earlier study, \textit{J. R. Sharma} and \textit{H. Arora} [Appl. Math. Lett. 29, 1--6 (2014; Zbl 1311.65051)] did not discuss these properties. Furthermore, the order of convergence was shown using Taylor series expansions and hypotheses up to the fourth order derivative or even higher of the function involved which restrict the applicability of the proposed scheme. However, only the first order derivatives appear in the proposed scheme. To overcome this problem, we present the hypotheses for the proposed scheme maximum up to first order derivative. In this way, we not only expand the applicability of the methods but also suggest convergence domain. Finally, a variety of concrete numerical examples are proposed where earlier studies can not be applied to obtain the solutions of nonlinear equations on the other hand our study does not exhibit this type of problem/restriction.
Mathematics Subject Classification ID: 65J15
zbMATH DE Number: 7042374
zbMATH Keywords: Kung-Traub method
zbMATH Keywords: local convergence
zbMATH Keywords: divided difference
zbMATH Keywords: Banach space
zbMATH Keywords: Lipschitz constant
zbMATH Keywords: radius of convergence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a9040065
OpenAlex ID: W2525583675
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DOI: 10.3390/A9040065
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description: scientific article; zbMATH DE number 7042374