Some efficient seventh-order derivative-free families in root-finding

Finding simple roots by seventh- and eighth-order derivative-free 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...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

A Derivative-Free Method of Eighth-Order For Finding Simple Root of Nonlinear Equations

In this paper we have constructed an optimal eighth-order method with four function evaluations to solve the nonlinear equations. The proposed method is a three-step method in which no derivative is required. Our scheme is optimal in the sense of Kung and Traub. Moreover, some test functions have been also included to confirm the superiority of the proposed method. At the end, we have presented...

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

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.    

Optimal eighth-order simple root-finders free from derivative

The calculation of derivatives of a function mostly takes up a great deal of time and even in some cases, such as the existing problems in engineering and optimization, is impossible to be evaluated directly. Accordingly, an accurate derivative-free class of three-step methods is suggested for solving ( ) = 0. The proposed three-step technique comprises four evaluations of the function per iter...