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An efficient three-step method to solve system of nonlinear equations

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  • Esmaeili, H.
  • Ahmadi, M.

Abstract

In this paper, we suggest a sixth order convergence three-step method to solve system of nonlinear equations. Every iteration of the method requires two function evaluations, two first Fréchet derivative evaluations and two matrix inversions. Hence, the efficiency index is 61/(2n+6n2+43n3), which is better than that of other sixth order methods. The advantages of the method lie in the feature that this technique not only achieves an approximate solution with high accuracy, but also improves the calculation speed. Also, under several mild conditions the convergence analysis of the proposed method is provided. An efficient error estimation is presented for the approximate solution. Numerical examples are included to demonstrate the validity and applicability of the method and the comparisons are made with the existing results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:1093-1101
    DOI: 10.1016/j.amc.2015.05.076
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    Cited by:

    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. 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.
    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. Ramandeep Behl & Ioannis K. Argyros & Jose Antonio Tenreiro Machado, 2020. "Ball Comparison between Three Sixth Order Methods for Banach Space Valued Operators," Mathematics, MDPI, vol. 8(5), pages 1-12, April.

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