A new sixth-order Steffensen-type iterative method for solving nonlinear equations (Q1637854)

Summary: Based on iterative method proposed by \textit{M. Basto} et al. [Appl. Math. Comput. 173, No. 1, 468--483 (2006; Zbl 1091.65043)], we present a new derivative-free iterative method for solving nonlinear equations. The aim of this paper is to develop a new method to find the approximation of the root \(\alpha \) of the nonlinear equation \(f(x)=0\). This method has the efficiency index which equals \(6^{1/4}=1.5651\). The benefit of this method is that this method does not need to calculate any derivative. Several examples illustrate that the efficiency of the new method is better than that of previous methods.