Local convergence of an efficient high convergence order method using hypothesis only on the first derivative
type: Item
instance of: scholarly article
title: Local convergence of an efficient high convergence order method using hypothesis only on the first derivative
zbMATH Open document ID: 1461.65099
author: Ioannis Konstantinos Argyros
author: Ramandeep Behl
author: Sandile Sydney Motsa
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: We present a local convergence analysis of an eighth order three step method in order to approximate a locally unique solution of nonlinear equation in a Banach space setting. In an earlier study by \textit{J. R. Sharma} and \textit{H. Arora} [Appl. Math. Comput. 273, 924--933 (2016; Zbl 1410.65173)], 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 first order derivative appears in the proposed scheme. In order to overcome this problem, we proposed the hypotheses up to only the first order derivative. In this way, we not only expand the applicability of the methods but also propose convergence domain. Finally, where earlier studies cannot be applied, a variety of concrete numerical examples are proposed to obtain the solutions of nonlinear equations. Our study does not exhibit this type of problem/restriction.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 7042301
zbMATH Keywords: Newton-like method
zbMATH Keywords: local convergence
zbMATH Keywords: efficiency index
zbMATH Keywords: optimum method
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a8041076
OpenAlex ID: W2178582914
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DOI: 10.3390/A8041076
description: scientific article; zbMATH DE number 7042301