A new three step iterative method for solving a nonlinear equation is introduced based on the following scheme: Let is an initial guess sufficiently close to simple root of the equation . The iterative step consists from two predictor steps:
and one corrector step:
The authors show that if the function is sufficiently differentiable in the open interval, which contain a simple root of the equation and if is sufficiently close to this root, then the proposed iterative algorithm has the order of convergence equal to three. Several numerical examples are given to illustrate the efficiency and performance of the new method.