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New two-parameter Chebyshev–Halley-like family of fourth and sixth-order methods for systems of nonlinear equations

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  • Narang, Mona
  • Bhatia, Saurabh
  • Kanwar, V.

Abstract

The two-parameter Chebyshev–Halley-like family of optimal two-point fourth-order methods proposed by Babajee (2015), is further extended to solve systems of nonlinear equations. This two-step fourth-order family is further extended to obtain a two-parameter family of sixth-order methods which requires only one extra function evaluation. The performance of some special members of the proposed families using only single inverse per iteration have been tested through numerical examples and the results show that these are effective and comparable to existing methods both in order and efficiency.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:394-403
    DOI: 10.1016/j.amc.2015.11.063
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    References listed on IDEAS

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    1. Rostamy, Davoud & Bakhtiari, Parisa, 2015. "New efficient multipoint iterative methods for solving nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 350-356.
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    Cited by:

    1. 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.
    2. Hessah Faihan Alqahtani & Ramandeep Behl & Munish Kansal, 2019. "Higher-Order Iteration Schemes for Solving Nonlinear Systems of Equations," Mathematics, MDPI, vol. 7(10), pages 1-14, October.
    3. Sharma, Janak Raj & Sharma, Rajni & Bahl, Ashu, 2016. "An improved Newton–Traub composition for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 98-110.
    4. José J. Padilla & Francisco I. Chicharro & Alicia Cordero & Alejandro M. Hernández-Díaz & Juan R. Torregrosa, 2024. "A Class of Efficient Sixth-Order Iterative Methods for Solving the Nonlinear Shear Model of a Reinforced Concrete Beam," Mathematics, MDPI, vol. 12(3), pages 1-16, February.
    5. Zhanlav, T. & Otgondorj, Kh., 2021. "Higher order Jarratt-like iterations for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    6. Beny Neta, 2021. "A Note on Traub’s Method for Systems of Nonlinear Equations," Mathematics, MDPI, vol. 9(23), pages 1-8, November.

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