Some New Three Step Iterative Methods for Solving Nonlinear Equation Using Steffensen’s and Halley Method

In this paper, we introduce the comparative study of new three step iterative methods for finding the zeros of the nonlinear equation f(x) = 0. The new method based on the Steffensen’s method and Halley method with using predictor – corrector technique. It is established that the new method (NTSM-1) has convergence order sixth and second new method (NTSM-2) has convergence order seventh. Numerical tests show that the new methods is comparable with the well known existing methods and gives better results.