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An Optimal Fourth Order Iterative Method for Solving Nonlinear Equations and Its Dynamics

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  • Rajni Sharma
  • Ashu Bahl

Abstract

We present a new fourth order method for finding simple roots of a nonlinear equation . In terms of computational cost, per iteration the method uses one evaluation of the function and two evaluations of its first derivative. Therefore, the method has optimal order with efficiency index 1.587 which is better than efficiency index 1.414 of Newton method and the same with Jarratt method and King’s family. Numerical examples are given to support that the method thus obtained is competitive with other similar robust methods. The conjugacy maps and extraneous fixed points of the presented method and other existing fourth order methods are discussed, and their basins of attraction are also given to demonstrate their dynamical behavior in the complex plane.

Suggested Citation

  • Rajni Sharma & Ashu Bahl, 2015. "An Optimal Fourth Order Iterative Method for Solving Nonlinear Equations and Its Dynamics," Journal of Complex Analysis, Hindawi, vol. 2015, pages 1-9, November.
    • Handle: RePEc:hin:jnljca:259167
    DOI: 10.1155/2015/259167
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    Cited by:

    1. Yanlin Tao & Kalyanasundaram Madhu, 2019. "Optimal Fourth, Eighth and Sixteenth Order Methods by Using Divided Difference Techniques and Their Basins of Attraction and Its Application," Mathematics, MDPI, vol. 7(4), pages 1-22, March.
    2. Liu, Dongjie & Liu, Chein-Shan, 2022. "Two-point generalized Hermite interpolation: Double-weight function and functional recursion methods for solving nonlinear equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 317-330.
    3. Prem B. Chand & Francisco I. Chicharro & Neus Garrido & Pankaj Jain, 2019. "Design and Complex Dynamics of Potra–Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications," Mathematics, MDPI, vol. 7(10), pages 1-21, October.

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