Sixth order derivative free family of iterative methods

In this study, we develop a four-parameter family of sixth order convergent iterative methods for solving nonlinear scalar equations. Methods of the family require evaluation of four functions per iteration. These methods are totally free of derivatives. Convergence analysis shows that the family is sixth order convergent, which is also verified through the numerical work. Though the methods are independent of derivatives, computational results demonstrate that family of methods are efficient and demonstrate equal or better performance as compared with other six order methods, and the classical Newton method.