A Derivative-Free Method of Eighth-Order For Finding Simple Root of Nonlinear Equations

In this paper we have constructed an optimal eighth-order method with four function evaluations to solve the non-linear equations. The proposed method is a three-step method in which no derivative is required. Our scheme is optimal in the sense of Kung and Traub. Moreover, some test functions have been also included to confirm the superiority of the proposed method. At the end, we have presented the basins of attraction of some existing methods along with our proposed method to illustrate their performances