Modified Potra-Pták method to determine the multiple zeros of nonlinear equations

Abstract

In this paper, we present a third-order iterative method based on Potra-Pt{á}k method to compute the approximate multiple roots of nonlinear equations. The method requires two evaluations of the function and one evaluation of its first derivative per iteration and it has the efficiency index equal to $3^{\frac{1}{3}}\approx 1.44225$. We describe the analysis of the proposed methods along with numerical experiments including comparison with existing methods. Moreover, the attraction basins are shown and compared with other existing methods.