relation: https://khub.utp.edu.my/scholars/11301/
title: Optimal fourth- and eighth-order of convergence derivative-free modifications of King's method
creator: Said Solaiman, O.
creator: Abdul Karim, S.A.
creator: Hashim, I.
description: Starting by King's method, we propose a modified families of fourth- and eighth-order of convergence iterative methods for nonlinear equations. The fourth-order method requires at each iteration three function evaluations, while the eighth-order methods both need four function evaluations. The proposed methods are derivative-free. Based on the conjecture of Kung and Traub, the new methods attain the optimality with efficiency index 1.587 for the fourth-order method and 1.68 for the eighth-order methods. The convergence analyses of the methods are given, and comparisons with some well-known schemes having identical order of convergence demonstrate the efficiency of the present techniques. © 2018 The Authors
publisher: Elsevier B.V.
date: 2019
type: Article
type: PeerReviewed
identifier:   Said Solaiman, O. and Abdul Karim, S.A. and Hashim, I.  (2019) Optimal fourth- and eighth-order of convergence derivative-free modifications of King's method.  Journal of King Saud University - Science, 31 (4).  pp. 1499-1504.  ISSN 10183647     
relation: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85057957375&doi=10.1016%2fj.jksus.2018.12.001&partnerID=40&md5=a70f1e060da4974c0d21debf73e325a0
relation: 10.1016/j.jksus.2018.12.001
identifier: 10.1016/j.jksus.2018.12.001