Fourth-order derivative-free methods for solving non-linear equations

Abstract

Two new one-parameter families of methods for finding simple and real roots of non-linear equations without employing derivatives of any order are developed. Error analysis providing the fourth-order convergence is given. Each member of the families requires three evaluations of function per step, and therefore the method has an efficiency index of 1.587. Numerical examples are presented and the performance of the method presented here is compared with methods available in the literature.