A derivative free iterative method for finding multiple roots of nonlinear equations

For an equation f(x)=0f(x)=0 having a multiple root of multiplicity m>1m>1 unknown, we propose a transformation which converts the multiple root to a simple root of Hϵ(x)=0Hϵ(x)=0. The transformed function Hϵ(x)Hϵ(x) of f(x)f(x) with a small ϵ>0ϵ>0 has appropriate properties in applying a derivative free iterative method to find the root. Moreover, there is no need to choose a proper initial approximation. We show that the proposed method is superior to the existing methods by several numerical examples.