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A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics

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  • Bahl, Ashu
  • Cordero, Alicia
  • Sharma, Rajni
  • R. Torregrosa, Juan

Abstract

In this paper, we propose a general bi-parametric family of sixth order iterative methods to solve systems of nonlinear equations. The presented scheme contains some well known existing methods as special cases. The stability of the proposed class, presented as an appendix, is used for selecting the most stable members of the family with optimum numerical performance. From the comparison with some existing methods of similar nature, it is observed that the presented methods show robust and efficient character.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:357:y:2019:i:c:p:147-166
    DOI: 10.1016/j.amc.2019.04.003
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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. Esmaeili, H. & Ahmadi, M., 2015. "An efficient three-step method to solve system of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1093-1101.
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    Cited by:

    1. Ramandeep Behl & Ioannis K. Argyros & Fouad Othman Mallawi & Sattam Alharbi, 2023. "Extended Seventh Order Derivative Free Family of Methods for Solving Nonlinear Equations," Mathematics, MDPI, vol. 11(3), pages 1-11, February.
    2. Zhanlav, T. & Otgondorj, Kh., 2021. "Higher order Jarratt-like iterations for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).

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