New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations

Somayeh Sharifi, et al. "New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations." Open Mathematics 14.1 (2016): 443-451. <http://eudml.org/doc/285654>.

@article{SomayehSharifi2016,
abstract = {In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari’s method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to [...] 814≈1.682$\{8^\{\{\textstyle \{1 \over 4\}\}\}\} \approx 1.682$. We describe the analysis of the proposed methods along with numerical experiments including comparison with the existing methods. Moreover, the attraction basins of the proposed methods are shown with some comparisons to the other existing methods.},
author = {Somayeh Sharifi, Massimiliano Ferrara, Mehdi Salimi, Stefan Siegmund},
journal = {Open Mathematics},
keywords = {Multi-point iterative methods; Maheshwari’s method; Kung and Traub’s conjecture; Basin of attraction; multi-point iterative methods; Maheshwari's method; Kung and Traub's conjecture; basin of attraction; convergence; simple roots; numerical experiment},
language = {eng},
number = {1},
pages = {443-451},
title = {New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations},
url = {http://eudml.org/doc/285654},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Somayeh Sharifi
AU - Massimiliano Ferrara
AU - Mehdi Salimi
AU - Stefan Siegmund
TI - New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 443
EP - 451
AB - In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari’s method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to [...] 814≈1.682${8^{{\textstyle {1 \over 4}}}} \approx 1.682$. We describe the analysis of the proposed methods along with numerical experiments including comparison with the existing methods. Moreover, the attraction basins of the proposed methods are shown with some comparisons to the other existing methods.
LA - eng
KW - Multi-point iterative methods; Maheshwari’s method; Kung and Traub’s conjecture; Basin of attraction; multi-point iterative methods; Maheshwari's method; Kung and Traub's conjecture; basin of attraction; convergence; simple roots; numerical experiment
UR - http://eudml.org/doc/285654
ER -