@article { author = {Ahmadi, Mehdi and Esmaeili, Hamid and Erfanifar, R}, title = {Solving System of Nonlinear Equations by using a New Three-Step Method}, journal = {Control and Optimization in Applied Mathematics}, volume = {1}, number = {2}, pages = {53-62}, year = {2016}, publisher = {Payame Noor University (PNU)}, issn = {2383-3130}, eissn = {2538-5615}, doi = {}, abstract = {In this paper‎, ‎we suggest a fifth order convergence three-step method for solving system of nonlinear equations‎. ‎Each iteration of the method requires two function evaluations‎, ‎two first Fr\'{e}chet derivative evaluations and two matrix inversions‎. ‎Hence‎, ‎the efficiency index is $5^{1/({2n+4n^{2}+\frac{4}{3}n^{3}})}$‎, ‎which is better than that of other three-step 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.}, keywords = {Nonlinear equations‎,‎Iterative method‎,‎Convergence order‎,‎Efficiency index}, url = {https://mathco.journals.pnu.ac.ir/article_3398.html}, eprint = {https://mathco.journals.pnu.ac.ir/article_3398_cee896e67e39e179b12bcb4a52ca7cc3.pdf} }