A family of the best iterative methods for systems of nonlinear equations
DOI:
https://doi.org/10.5564/mmj.v26i1.5002Keywords:
mathAbstract
In this paper, we develop an iterative method with scalar and vector coefficients, exhibiting convergence orders (4 ≤ ρ ≤ 8) for solving nonlinear systems and further extend it to m-step formulations. All of these methods require only a single inversion of the Jacobian matrix per iteration. We define concepts such as best iterative methods, which require a minimum total cost, allowing us to classify both new and existing methods in terms of their effectiveness. The computational efficiency of the proposed techniques is discussed and compared with existing methods. Moreover, the basin of attraction method is studied for nonlinear systems to validate our findings and identify the most effective methods, while a dynamical analysis confirms the scheme’s superior stability and extensive convergence regions. Finally, numerical experiments confirm and validate the theoretical results and demonstrate their effectiveness.
Mathematics Subject Classification: 65H05,65D05.
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Copyright (c) 2025 Tugal Zhanlav, Khuder Otgondorj, Khangai Enkhbayar
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