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Three-step iterative methods for numerical solution of systems of nonlinear equations

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Abstract

In this paper, we introduce seventh- and sixth-order methods for solving the systems of nonlinear equations. The convergence analysis of the proposed methods is provided. The computational efficiency for these methods is \( 6^{1/(3n+2n^2)} \) and \( 7^{1/(4n+2n^2)} \). Computational efficiency of new methods is compared with Newton’s method and some other recently published methods. Numerical examples are included to demonstrate the validity and applicability of the methods and comparison is made with the existing results.

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Acknowledgements

The authors extend their appreciation to reviewers for their valuable suggestions to revise this paper.

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  1. Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, 15914, Iran

    Mehdi Dehghan & Akbar Shirilord

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  1. Mehdi Dehghan
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  2. Akbar Shirilord
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Correspondence to Mehdi Dehghan.

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Dehghan, M., Shirilord, A. Three-step iterative methods for numerical solution of systems of nonlinear equations. Engineering with Computers 38, 1015–1028 (2022). https://doi.org/10.1007/s00366-020-01072-1

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  • DOI: https://doi.org/10.1007/s00366-020-01072-1

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