TY - JOUR
ID - 3398
TI - Solving System of Nonlinear Equations by using a New Three-Step Method
JO - Control and Optimization in Applied Mathematics
JA - COAM
LA - en
SN - 2383-3130
AU - Ahmadi, Mehdi
AU - Esmaeili, Hamid
AU - Erfanifar, R
AD - Department of Mathematics, Malayer University, Malayer, Iran.
AD - Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran.
Y1 - 2016
PY - 2016
VL - 1
IS - 2
SP - 53
EP - 62
KW - Nonlinear equations
KW - Iterative method
KW - Convergence order
KW - Efficiency index
DO -
N2 - 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.
UR - https://mathco.journals.pnu.ac.ir/article_3398.html
L1 - https://mathco.journals.pnu.ac.ir/article_3398_cee896e67e39e179b12bcb4a52ca7cc3.pdf
ER -