In this paper, a family of derivative-free methods of cubic convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.442. The convergence and error analysis are given. Also, numerical examples are used to show the performance of the presented methods and to compare with other derivative-free methods. And, were applied these methods on smooth and nonsmooth equations.
The Bulletin of Society for Mathematical Services and Standards (Volume 3)
M.S.M. Bahgat and M.A. Hafiz, "Solving Nonsmooth Equations Using Derivative-Free Methods", The Bulletin of Society for Mathematical Services and Standards, Vol. 3, pp. 37-45, 2012