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Derivative-Free Iterative Schemes for Multiple Roots of Nonlinear Functions

Author

Listed:
  • Himani Arora

    (Department of Mathematics, Guru Nanak Dev University, Amritsar 143005, India)

  • Alicia Cordero

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain)

  • Juan R. Torregrosa

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain)

  • Ramandeep Behl

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Sattam Alharbi

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

The construction of derivative-free iterative methods for approximating multiple roots of a nonlinear equation is a relatively new line of research. This paper presents a novel family of one-parameter second-order techniques. Our schemes are free from derivatives and have been designed to find multiple roots ( m ≥ 2 ). The new techniques involve the weight function approach. The convergence analysis for the new family is presented in the main theorem. In addition, some special cases of the new class are discussed. We also illustrate the applicability of our methods on van der Waals, Planck’s radiation, root clustering, and eigenvalue problems. We also contrast them with the known methods. Finally, the dynamical study of iterative schemes also provides a good overview of their stability.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1530-:d:807710
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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. Munish Kansal & Ali Saleh Alshomrani & Sonia Bhalla & Ramandeep Behl & Mehdi Salimi, 2020. "One Parameter Optimal Derivative-Free Family to Find the Multiple Roots of Algebraic Nonlinear Equations," Mathematics, MDPI, vol. 8(12), pages 1-15, December.
    3. 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.
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