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

For an equation f ( x ) = 0 having a multiple root of multiplicity m > 1 unknown, we propose a transformation which converts the multiple root to a simple root of H ϵ ( x ) = 0 . The transformed function H ϵ ( x ) of f ( x ) with a small ϵ > 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.