Optimal fourth- and eighth-order of convergence derivative-free modifications of King's method

Obadah Said Solaiman, Samsul Ariffin Abdul Karim, Ishak Hashim

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
JournalJournal of King Saud University - Science
DOIs
Publication statusAccepted/In press - 1 Jan 2018

Fingerprint

Derivative-free
Order of Convergence
Evaluation Function
Fourth Order
Efficiency Index
Iteration
Optimality
Nonlinear Equations

Keywords

  • Iterative method
  • King's method
  • Nonlinear equations
  • Order of convergence
  • Root finding method

ASJC Scopus subject areas

  • General

Cite this

Optimal fourth- and eighth-order of convergence derivative-free modifications of King's method. / Said Solaiman, Obadah; Abdul Karim, Samsul Ariffin; Hashim, Ishak.

In: Journal of King Saud University - Science, 01.01.2018.

Research output: Contribution to journalArticle

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