Document Type : Research Article

Authors

• Mehdi Ahmadi ¹
• Hamid Esmaeili ²
• R Erfanifar ²

¹ Department of Mathematics, Malayer University, Malayer, Iran.

² Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran.

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

Main Subjects

• Related Topics