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

Author

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  • Malik Zaka Ullah
  • A. S. Al-Fhaid
  • Fayyaz Ahmad

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(= ) 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.

Suggested Citation

  • Malik Zaka Ullah & A. S. Al-Fhaid & Fayyaz Ahmad, 2013. "Four-Point Optimal Sixteenth-Order Iterative Method for Solving Nonlinear Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-5, September.
    • Handle: RePEc:hin:jnljam:850365
    DOI: 10.1155/2013/850365
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    Cited by:

    1. Uriel Filobello-Nino & Hector Vazquez-Leal & Jesús Huerta-Chua & Jaime Martínez-Castillo & Agustín L. Herrera-May & Mario Alberto Sandoval-Hernandez & Victor Manuel Jimenez-Fernandez, 2022. "The Enhanced Fixed Point Method: An Extremely Simple Procedure to Accelerate the Convergence of the Fixed Point Method to Solve Nonlinear Algebraic Equations," Mathematics, MDPI, vol. 10(20), pages 1-19, October.

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