%0 Journal Article
%@ 10183647
%A Said Solaiman, O.
%A Abdul Karim, S.A.
%A Hashim, I.
%D 2019
%F scholars:11301
%I Elsevier B.V.
%J Journal of King Saud University - Science
%N 4
%P 1499-1504
%R 10.1016/j.jksus.2018.12.001
%T Optimal fourth- and eighth-order of convergence derivative-free modifications of King's method
%U https://khub.utp.edu.my/scholars/11301/
%V 31
%X 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
%Z cited By 14