Family of Optimal Eighth-Order of Convergence for Solving Nonlinear Equations

In this paper, a new family of optimal eighth-order iterative methods are presented. The new family is developed by combining Traub-Ostrowski’s fourth-order method adding Newton’s method as a third step and using the forward divided difference and three real-valued functions in the third step to reduce the number of function evaluations. We employed several numerical comparisons to demonstrate the performance of the proposed method