# An optimal family of methods for obtaining the zero of nonlinear equation

Document Type : Original Article

Authors

1 Department of mathematics and statistics, Faculty of science, Delta state University of science and technology, ozoro, Delta state, Nigeria.

2 Department of General studies, Petroleum Training Institute, Effurun, Delta State, Nigeria.

Abstract

This manuscript presents a developed fourth-order iterative family
of methods for determining the zero of nonlinear equations that is
optimal in line with Kung-Traub conjecture. The family of methods
was constructed by using weight function technique. One iteration
cycle of any concrete member of the family of methods requires the
evaluation of three functions. Consequently, the efficiency index of any
concrete member of the family is 1.5873. The method convergence
analysis was carried out via the Taylor series technique and numerical
examples are provided to illustrate its performance as compared with
its contemporary existing methods for obtaining the zero of nonlinear
equation.

Keywords

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### History

• Receive Date: 31 October 2021
• Revise Date: 05 February 2022
• Accept Date: 09 February 2022
• First Publish Date: 09 February 2022