Journal of Applied Mathematics

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

Malik Zaka Ullah, A. S. Al-Fhaid, and Fayyaz Ahmad

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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(=25-1) 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

Permanent link to this document
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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References

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