Third order convergence iterative method for multiple roots of nonlinear equation

We present a new third order convergence iterative method for solving multiple roots of nonlinear equation, which requires one function evaluation and two evaluation of first derivative of function per step. Our present method free from second derivative function. Error term is proved to possess a third order method. Numerical experiments exhibit that our method gives the smallest error of bound per iteration and it is highly accurate as compared to other existing iterative methods