New formulation of third and sixth order iterative methods for solving nonlinear equations

Finding the zeros of a nonlinear equation f (x) = 0, is a classical problem which has nice applications in various branches of science and engineering. In this paper, we introduce two iterative methods which are based on the Modified Simpson's approximations to definite integral in Newton theorem. It is proved that first method have cubic convergence and second method have six convergence. In order to demonstrate the convergence properties of the introduced methods, several numerical examples are given.