## Journal of Applied Mathematics

### Four-Point Optimal Sixteenth-Order Iterative Method for Solving Nonlinear Equations

#### Abstract

We present an iterative method for solving nonlinear equations. The proposed iterative method has optimal order of convergence sixteen in the sense of Kung-Traub conjecture (Kung and Traub, 1974); it means that the iterative scheme uses five functional evaluations to achieve 16(=${2}^{5-1}$) order of convergence. The proposed iterative method utilizes one derivative and four function evaluations. Numerical experiments are made to demonstrate the convergence and validation of the iterative method.

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 850365, 5 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808114

Digital Object Identifier
doi:10.1155/2013/850365

Mathematical Reviews number (MathSciNet)
MR3096062

Zentralblatt MATH identifier
06950907

#### Citation

Ullah, Malik Zaka; Al-Fhaid, A. S.; Ahmad, Fayyaz. Four-Point Optimal Sixteenth-Order Iterative Method for Solving Nonlinear Equations. J. Appl. Math. 2013 (2013), Article ID 850365, 5 pages. doi:10.1155/2013/850365. https://projecteuclid.org/euclid.jam/1394808114

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