An Optimal Class of Eighth-Order Iterative Methods Based on King’s Method

  • Ibrahim Ahmed Al-Subaihi Department of Mathematics, Faculty of Science, Taibah University, Saudi Arabia
  • T. GH. Al-Harbi Department of Mathematics, Faculty of Science, Taibah University, Saudi Arabia
Keywords: iterative method, optimal method, nonlinear equations, order of convergence.

Abstract

This paper based on King’s fourth order methods. A class of eighth-order methods is presented for solving simple roots of nonlinear equations. The class is developed by combining King’s fourth-order  method and Newton’s method as a third step using the forward divided difference and multiplication of  three weight function. Some numerical comparisons have been considered to show the performance of the proposed method.

Downloads

Download data is not yet available.

References

I. A. Al-subaihi, A. J. Alqarni. Higher-Order Iterative Methods for Solving Nonlinear Equations, Life Science Journal, 11, 12, pp. 85-91, 2014.

Al-Harbi, I.A. Al-Subaihi. Family of Optimal Eighth-Order of Convergence for Solving Nonlinear Equations, 2015.

W. Bi, Q. Wu, H. Ren, A new family of eighth-order iterative methods for solving nonlinear equations, Appl. Math.214, pp.236–245, 2009.

C. Chun, B.Neta, An analysis of a new family of eighth-order optimal methods, Appl. Math. Comput. 245(2014), 86–107.

C. Lee, Chun, M.Y. A new optimal eighth-order family of iterative methods for the solution of nonlinear equations. Appl. Math. Comput., 223: 506–519 (2013).

A. Cordero, J. R. Torregrosa, and M. P. Vassileva, “Three-step iterative methods with optimal eighthorder convergence,” Journal of Computational and Applied Mathematics, vol. 235, no. 10, pp. 3189–3194, 2011.

W. Gautschi, Numerical Analysis, An Introduction,Birkhauser, Barton, Mass, USA, 1997.

R. F. King, “A family of fourth order methods for nonlinear equations,” SIAM Journal on Numerical Analysis, vol. 10, pp. 876–879, 1973.

H. T. Kung and J. F. Traub, “Optimal order of one-point and multipoint iteration,” Journal of the Association for Computing Machinery, 21, pp. 643–651, 1974 .

L. Liu, X. Wang, Eighth-order methods with high efficiency index for solving nonlinear equations, Applied Mathematics and Computation, 215, pp.3449-3454, 2010.

S. Miodrag Petkovic, Ljiljana D. Petkovic, Families Of Optimal Multipoint Method For Solving Nonlinear Equations: A SURVEY, Appl. Anal. Discrete Math. 4, pp.1-22, 2010.

A.M. Ostrowski, Solution of Equations in Euclidean and Banach Spaces, Academic Press, New York, 1960.

R. Sharma, Sharma, A new family of modified Ostrowski’s methods with accelerated eighth order convergence, Numerical Algorithms, 54, pp. 445-458, 2010.

J. Traub, Iterative methods for the solution of equations, American Mathematical Soc, 1982.

S. Weerakoon, G. I. Fernando. A variant of Newton’s method with accelerated third-order convergence, Appl. Math. Lett., 17, 8, pp.87-93, 2000 .

Zhanlav, V. Ulziibayar. Modified King's Methods with Optimal Eighth-order of Convergence and High Efficiency Index, American Journal of Computational and Applied Mathematics, 2016 .

Published
2018-06-20
How to Cite
Al-Subaihi, I., & Al-Harbi, T. (2018). An Optimal Class of Eighth-Order Iterative Methods Based on King’s Method. Journal of Progressive Research in Mathematics, 13(3), 2329-2336. Retrieved from https://scitecresearch.com/journals/index.php/jprm/article/view/1556
Section
Articles