<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Department of Mathematical Sciences, Cameron University, Lawton, OK 73505,

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

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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...

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

Published Online: Sep 24, 2016

Page range: 3 - 16

Received: Mar 03, 2016

Accepted: Mar 21, 2016

DOI: https://doi.org/10.1515/awutm-2016-0001

Keywords
Nonlinear equation, Optimal efficiency index, Local convergence, Eighth order of convergence

© 2016 Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Sep 24, 2016

Page range: 3 - 16

Received: Mar 03, 2016

Accepted: Mar 21, 2016

DOI: https://doi.org/10.1515/awutm-2016-0001

KeywordsNonlinear equation, Optimal efficiency index, Local convergence, Eighth order of convergence

© 2016 Annals of West University of Timisoara - Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Nonlinear equation, Optimal efficiency index, Local convergence, Eighth order of convergence