An Optimal Fourth Order Derivative-Free Numerical Algorithm for Multiple Roots

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.    

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.

New Families of Fourth-Order Derivative-Free Methods for Solving Nonlinear Equations with Multiple Roots

In this paper, two new fourth-order derivative-free methods for finding multiple zeros of nonlinear equations are presented. In terms of computational cost the family requires three evaluations of functions per iteration. It is proved that the each of the methods has a convergence of order four. In this way it is demonstrated that the proposed class of methods supports the Kung-Traub hypothesis...

Basins of attraction for several optimal fourth order methods for multiple roots

There are very few optimal fourth order methods for solving nonlinear algebraic equations having roots of multiplicity m. Here we compare five such methods, two of which require the evaluation of the (m − 1)st root. The methods are usually compared by evaluating the computational efficiency and the efficiency index. In this paper all the methods have the same efficiency, since they are of the s...

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