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Optimal One-Point Iterative Function Free from Derivatives for Multiple Roots

Author

Listed:
  • Deepak Kumar

    (Department of Mathematics, Chandigarh University, Gharuan, Mohali, Punjab 140413, India)

  • Janak Raj Sharma

    (Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, Punjab 148106, India)

  • Ioannis K. Argyros

    (Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA)

Abstract

We suggest a derivative-free optimal method of second order which is a new version of a modification of Newton’s method for achieving the multiple zeros of nonlinear single variable functions. Iterative methods without derivatives for multiple zeros are not easy to obtain, and hence such methods are rare in literature. Inspired by this fact, we worked on a family of optimal second order derivative-free methods for multiple zeros that require only two function evaluations per iteration. The stability of the methods was validated through complex geometry by drawing basins of attraction. Moreover, applicability of the methods is demonstrated herein on different functions. The study of numerical results shows that the new derivative-free methods are good alternatives to the existing optimal second-order techniques that require derivative calculations.

Suggested Citation

  • Deepak Kumar & Janak Raj Sharma & Ioannis K. Argyros, 2020. "Optimal One-Point Iterative Function Free from Derivatives for Multiple Roots," Mathematics, MDPI, vol. 8(5), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:709-:d:353607
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    References listed on IDEAS

    as
    1. Geum, Young Hee & Kim, Young Ik & Neta, Beny, 2015. "A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 387-400.
    2. Deepak Kumar & Janak Raj Sharma & Clemente Cesarano, 2019. "One-Point Optimal Family of Multiple Root Solvers of Second-Order," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
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    Cited by:

    1. Himani Arora & Alicia Cordero & Juan R. Torregrosa & Ramandeep Behl & Sattam Alharbi, 2022. "Derivative-Free Iterative Schemes for Multiple Roots of Nonlinear Functions," Mathematics, MDPI, vol. 10(9), pages 1-13, May.

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