New modification of Maheshwari method with optimal eighth order of   convergence for solving nonlinear equations
  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 method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. This class of methods has the efficiency index equal to $8^{\frac{1}{4}}\approx 1.682$. We describe the analysis of the proposed methods along with numerical experiments including comparison with existing methods. 
Somayeh Sharifi, Massimiliano Ferrara, Mehdi Salimi, Stefan Seigmund
math.NA