Some Higher-Order Families of Methods for Finding Simple Roots of Nonlinear Equations

In this paper, a new fifth-order family of methods free from second derivative is obtained. This new iterative family contains the King’s family, which is one of the most well-known family of methods for solving nonlinear equations, and some other known methods as its particular case. To illustrate the efficiency and performance of proposed family, several numerical examples are presented. Numerical results illustrate better efficiency and performance of the presented methods in comparison with the other compared fifth-order methods. Due to that, they can be effectively used for solving nonlinear equations.