SOME DERIVATIVE FREE ITERATIVE METHODS FOR SOLVING NONLINEAR EQUATIONS

In this paper we present two new derivative free iterative methods for finding the zeros of the nonlinear equation f(x) = 0. Finding the zeros of the nonlinear equations is a classical problem in numerical analysis arises frequently in various branches of science and engineering. The aim of this paper is to develop some efficient methods to find the approximation of the root ù of the nonlinearequation f(x) = 0, without the evaluation of the derivatives. The new methods based on the centraldifferenceand forward-difference approximations to derivatives. It is proved that one of the methodshas cubic convergence and other method has fourth-order convergence. The benefit of these methods is that these methods do not need to calculate any derivative. Several examples illustrate that theconvergence and efficiency of the new methods are better than previous methods.