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Higher order Jarratt-like iterations for solving systems of nonlinear equations

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  • Zhanlav, T.
  • Otgondorj, Kh.

Abstract

In this article, we propose a new family of methods, such as Jarratt, with the fifth and sixth order. This includes some popular methods as special cases. We propose four different selection for parameter matrix Tk. The main advantage of the proposed methods is that they work well for any value of parameter “a” in the first stage of iterations, while the existing methods work only for some a(2/3or1/2). Thus, we extend essentially the domain of applicability of the original ones. Based on the computational efficiency analysis, we also made a selection of some high-efficiency ones among the families.

Suggested Citation

  • Zhanlav, T. & Otgondorj, Kh., 2021. "Higher order Jarratt-like iterations for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    • Handle: RePEc:eee:apmaco:v:395:y:2021:i:c:s009630032030802x
    DOI: 10.1016/j.amc.2020.125849
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    References listed on IDEAS

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    1. Abbasbandy, Saeid & Bakhtiari, Parisa & Cordero, Alicia & Torregrosa, Juan R. & Lotfi, Taher, 2016. "New efficient methods for solving nonlinear systems of equations with arbitrary even order," Applied Mathematics and Computation, Elsevier, vol. 287, pages 94-103.
    2. Zhanlav, T. & Chuluunbaatar, O. & Ulziibayar, V., 2017. "Generating function method for constructing new iterations," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 414-423.
    3. Narang, Mona & Bhatia, Saurabh & Kanwar, V., 2016. "New two-parameter Chebyshev–Halley-like family of fourth and sixth-order methods for systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 394-403.
    4. Sharma, Janak Raj & Sharma, Rajni & Kalra, Nitin, 2015. "A novel family of composite Newton–Traub methods for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 520-535.
    5. H. Montazeri & F. Soleymani & S. Shateyi & S. S. Motsa, 2012. "On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, November.
    6. Bahl, Ashu & Cordero, Alicia & Sharma, Rajni & R. Torregrosa, Juan, 2019. "A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 147-166.
    7. Xiao, Xiaoyong & Yin, Hongwei, 2015. "A new class of methods with higher order of convergence for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 300-309.
    8. Chun, Changbum & Neta, Beny, 2019. "Developing high order methods for the solution of systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 178-190.
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    Cited by:

    1. Michael I. Argyros & Ioannis K. Argyros & Samundra Regmi & Santhosh George, 2022. "Generalized Three-Step Numerical Methods for Solving Equations in Banach Spaces," Mathematics, MDPI, vol. 10(15), pages 1-28, July.
    2. Ramandeep Behl & Ioannis K. Argyros & Fouad Othman Mallawi & Samaher Khalaf Alharbi, 2022. "Extending the Applicability of Highly Efficient Iterative Methods for Nonlinear Equations and Their Applications," Mathematics, MDPI, vol. 11(1), pages 1-18, December.

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