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Generalization of Liu–Zhou Method for Multiple Roots of Applied Science Problems

Author

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  • Sunil Kumar

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

  • Monika Khatri

    (Faculty of Management and Commerce, Poornima University, Jaipur 303905, India)

  • Muktak Vyas

    (Faculty of Management and Commerce, Poornima University, Jaipur 303905, India)

  • Ashwini Kumar

    (Faculty of Engineering and Technology, Poornima University, Jaipur 303905, India)

  • Priti Dhankhar

    (Department of Mathematics, Government College, Hisar 125001, India)

  • Lorentz Jäntschi

    (Department of Physics and Chemistry, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania)

Abstract

Some optimal and non-optimal iterative approaches for computing multiple zeros of nonlinear functions have recently been published in the literature when the multiplicity θ of the root is known. Here, we present a new family of iterative algorithms for multiple zeros that are distinct from the existing approaches. Some special cases of the new family are presented and it is found that existing Liu-Zhou methods are the special cases of the new family. To check the consistency and stability of the new methods, we consider the continuous stirred tank reactor problem, isentropic supersonic flow problem, eigenvalue problem, complex root problem, and standard test problem in the numerical section and we find that the new methods are more competitive with other existing fourth-order methods. In the numerical section, the error of the new methods confirms their robust character.

Suggested Citation

  • Sunil Kumar & Monika Khatri & Muktak Vyas & Ashwini Kumar & Priti Dhankhar & Lorentz Jäntschi, 2025. "Generalization of Liu–Zhou Method for Multiple Roots of Applied Science Problems," Mathematics, MDPI, vol. 13(3), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:523-:d:1584151
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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. Sharma, Janak Raj & Kumar, Sunil, 2021. "An excellent numerical technique for multiple roots," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 316-324.
    3. 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.
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