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An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros

Author

Listed:
  • Ramandeep Behl

    (Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    All authors contributed equally to this work.)

  • Sonia Bhalla

    (Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, Punjab, India
    All authors contributed equally to this work.)

  • Ángel Alberto Magreñán

    (Department of Mathematics and Mathematics, University of La Rioja, Madre de Dios 53, 26006 Logroño (La Rioja), Spain
    All authors contributed equally to this work.)

  • Alejandro Moysi

    (Department of Mathematics and Mathematics, University of La Rioja, Madre de Dios 53, 26006 Logroño (La Rioja), Spain
    All authors contributed equally to this work.)

Abstract

In this manuscript, we introduce the higher-order optimal derivative-free family of Chebyshev–Halley’s iterative technique to solve the nonlinear equation having the multiple roots. The designed scheme makes use of the weight function and one parameter α to achieve the fourth-order of convergence. Initially, the convergence analysis is performed for particular values of multiple roots. Afterward, it concludes in general. Moreover, the effectiveness of the presented methods are certified on some applications of nonlinear equations and compared with the earlier derivative and derivative-free schemes. The obtained results depict better performance than the existing methods.

Suggested Citation

  • Ramandeep Behl & Sonia Bhalla & Ángel Alberto Magreñán & Alejandro Moysi, 2021. "An Optimal Derivative Free Family of Chebyshev–Halley’s Method for Multiple Zeros," Mathematics, MDPI, vol. 9(5), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:546-:d:510892
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    References listed on IDEAS

    as
    1. Behl, Ramandeep & Cordero, Alicia & Motsa, S.S. & Torregrosa, Juan R., 2015. "On developing fourth-order optimal families of methods for multiple roots and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 520-532.
    2. Lotfi, T. & Magreñán, Á.A. & Mahdiani, K. & Javier Rainer, J., 2015. "A variant of Steffensen–King’s type family with accelerated sixth-order convergence and high efficiency index: Dynamic study and approach," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 347-353.
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