in this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. each of them requires one evaluation of the function and two of its first derivative per iteration. several numerical examples are given to illustrate the performance of the presented methods.

Nonlinear equation solving by without memory iterative methods is taken into account in the present research. Recently, Khattri and Argyros in [S.K. Khattri, I.K. Argyros, Sixth order derivative free family of iterative methods, Appl. Math. Comput. 217 (2011), 5500-5507], proposed a sixth-order family of derivative-free methods including four function evaluations per full cycle to reach the ind...

In this paper, seventh-order iterative methods for the solution ofnonlinear equations are presented. The new iterative methods are developed byusing weight function method and using an approximation for the last derivative,which reduces the required number of functional evaluations per step. Severalexamples are given to illustrate the eciency and the performance of the newiterative methods.