Modified iterative methods with cubic convergence for solving nonlinear equations

In this paper, we suggest and analyze two new predictor–corrector methods for solving nonlinear equations f(x) = 0. These methods can be considered as two-step methods. We show that these methods have cubic convergence. Using this one of the new methods, real or complex roots for certain nonlinear equations can be obtained. Several numerical examples are given to illustrate the efficiency and performance of the new methods. Our method can be considered as an improvement of the existing methods and can be viewed as an alternative to the existing methods.