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On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence

Author

Listed:
  • Janak Raj Sharma

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

  • Sunil Kumar

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

  • Lorentz Jäntschi

    (Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania
    Institute of Doctoral Studies, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania)

Abstract

A number of optimal order multiple root techniques that require derivative evaluations in the formulas have been proposed in literature. However, derivative-free optimal techniques for multiple roots are seldom obtained. By considering this factor as motivational, here we present a class of optimal fourth order methods for computing multiple roots without using derivatives in the iteration. The iterative formula consists of two steps in which the first step is a well-known Traub–Steffensen scheme whereas second step is a Traub–Steffensen-like scheme. The Methodology is based on two steps of which the first is Traub–Steffensen iteration and the second is Traub–Steffensen-like iteration. Effectiveness is validated on different problems that shows the robust convergent behavior of the proposed methods. It has been proven that the new derivative-free methods are good competitors to their existing counterparts that need derivative information.

Suggested Citation

  • Janak Raj Sharma & Sunil Kumar & Lorentz Jäntschi, 2020. "On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence," Mathematics, MDPI, vol. 8(7), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1091-:d:379940
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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.
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    Cited by:

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    2. Ramandeep Behl, 2022. "A Derivative Free Fourth-Order Optimal Scheme for Applied Science Problems," Mathematics, MDPI, vol. 10(9), pages 1-17, April.

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