Research Article
A New Sixteenth Order Iterative Method for Solving Nonlinear Equations
* Corresponding author
Abstract
In this paper, we present a new iterative method for solving nonlinear equations. The method is a combination of the method of Chun and the method of Hu et.al. The new method requires six function evaluations and has the order of convergence sixteenth. Numerical experiments are made to demonstrate the convergence and validation of the iterative method.
How to Cite
K. Wongsim, N. Srisarakham, A New Sixteenth Order Iterative Method for Solving Nonlinear Equations, Int. J. Anal. Appl. 23 (2025), 282. https://doi.org/10.28924/2291-8639-23-2025-282
BibTeX
@article{Wongsim2025,
author = {Wongsim, Kedsadaphon and Srisarakham, Napassanan},
title = {A New Sixteenth Order Iterative Method for Solving Nonlinear Equations},
journal = {Int. J. Anal. Appl.},
volume = {23},
year = {2025},
pages = {282},
doi = {10.28924/2291-8639-23-2025-282}
}References
- [1] J.F. Traub, Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, 1964.
- [2] R.F. King, A Family of Fourth Order Methods for Nonlinear Equations, SIAM J. Numer. Anal. 10 (1973), 876–879. https://doi.org/10.1137/0710072.
- [3] C. Chun, Some Variants of King's Fourth-Order Family of Methods for Nonlinear Equations, Appl. Math. Comput. 190 (2007), 57–62. https://doi.org/10.1016/j.amc.2007.01.006.
- [4] Z. Hu, L. Guocai, L. Tian, An Iterative Method with Ninth-Order Convergence for Solving Nonlinear Equations, Int. J. Contemp. Math. Sci. 6 (2011), 17–23.
- [5] W. Gautschi, Numerical Analysis: An Introduction, Birkhauser, 1997.
- [6] F. Zafar, N. Hussain, Z. Fatimah, A. Kharal, Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots, Sci. World J. 2014 (2014), 410410. https://doi.org/10.1155/2014/410410.
- [7] C. Comemuang, P.Janngam, Sixteenth-Order Iterative Method for Solving Nonlinear Equations, Int. J. Math. Comput. Sci. 17 (2022), 1039–1049.
- [8] J.R. Sharma, R.K. Guha, P. Gupta, Improved King’s Methods with Optimal Order of Convergence Based on Rational Approximations, Appl. Math. Lett. 26 (2013), 473–480. https://doi.org/10.1016/j.aml.2012.11.011.
- [9] F. Soleymani, S. Shateyi, H. Salmani, Computing Simple Roots by an Optimal Sixteenth‐Order Class, J. Appl. Math. 2012 (2012), 958020. https://doi.org/10.1155/2012/958020.