Payame Noor University (PNU) Control and Optimization in Applied Mathematics 2383-3130 1 2 2016 12 01 Solving System of Nonlinear Equations by using a New Three-Step Method حل دستگاه معادلات غیرخطی با استفاده از یک روش سه گامی جدید 53 62 3398 EN Mehdi Ahmadi Department of Mathematics, Malayer University, Malayer, Iran. Hamid Esmaeili Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran. R Erfanifar Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran. Journal Article 2015 11 13 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. https://mathco.journals.pnu.ac.ir/article_3398_cee896e67e39e179b12bcb4a52ca7cc3.pdf