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An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics

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  • Anuradha Singh
  • J. P. Jaiswal

Abstract

The prime objective of this paper is to design a new family of optimal eighth-order iterative methods by accelerating the order of convergence of the existing seventh-order method without using more evaluations for finding simple root of nonlinear equations. Numerical comparisons have been carried out to demonstrate the efficiency and performance of the proposed method. Finally, we have compared new method with some existing eighth-order methods by basins of attraction and observed that the proposed scheme is more efficient.

Suggested Citation

  • Anuradha Singh & J. P. Jaiswal, 2014. "An Efficient Family of Optimal Eighth-Order Iterative Methods for Solving Nonlinear Equations and Its Dynamics," Journal of Mathematics, Hindawi, vol. 2014, pages 1-14, September.
    • Handle: RePEc:hin:jjmath:569719
    DOI: 10.1155/2014/569719
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    References listed on IDEAS

    as
    1. Neta, Beny & Chun, Changbum, 2014. "Basins of attraction for several optimal fourth order methods for multiple roots," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 103(C), pages 39-59.
    2. Alicia Cordero & Fazlollah Soleymani & Juan R. Torregrosa & Stanford Shateyi, 2014. "Basins of Attraction for Various Steffensen-Type Methods," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-17, March.
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