On the Local Convergence of an Eighth-order Method for Solving Nonlinear Equations-Reference-Cited by-同舟云学术

On the Local Convergence of an Eighth-order Method for Solving Nonlinear Equations

Published:2016-07-01 Issue:1 Volume:54 Page:3-16
ISSN:1841-3307
Container-title:Annals of West University of Timisoara - Mathematics and Computer Science
language:en
Short-container-title:

Author:

Argyros Ioannis K.¹,Kansal Munish²,Kanwar V.²

Affiliation:

1. Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, United States of America

2. University Institute of Engineering and Technology, Panjab University, Chandigarh-160-014, India

Abstract

Abstract We present a local convergence analysis of an eighth-order method for approximating a locally unique solution of a non-linear equation. Earlier studies such as have shown convergence of these methods under hypotheses up to the seventh derivative of the function although only the first derivative appears in the method. In this study, we expand the applicability of these methods using only hypotheses up to the first derivative of the function. This way the applicability of these methods is extended under weaker hypotheses. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.

Publisher

Walter de Gruyter GmbH

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