Higher-Order Iterative Methods for Solving Nonlinear Equations

Abstract: In this report, we presented three high-order iterative methods for solving nonlinear equations of the form 0 = ) (x f . These proposed iterative methods are obtained by combining a fourth-order iterative method with the classical Newton's method and approximating the first derivative in the third step by three different approaches of combinations of previously evaluated function values. The convergence analyses of the new methods are discussed, and several examples are given to illustrate the methods' efficiency