Affiliation:
1. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Abstract
An optimal eighth-order multipoint numerical iterative method is constructed to find the
simple root of scalar nonlinear equations. It is a three-point numerical iterative method that uses three evaluations of func-tion f(¢) associated with a scalar nonlinear equation and one of its deriv-atives f0 (¢). The four functional evaluations are required to achieve the eighth-order convergence. According to Kung-Traub conjecture (KTC), an iterative numerical multipoint method without memory can achieve maximum order of convergence 2n¡1 where n is the total number of func-tion evaluations in a single instance of the method. Therefore, following the KTC, the proposed method in this article is
optimal.
Publisher
Department of Mathematics, University of the Punjab
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