A derivative free iterative method for finding multiple roots of nonlinear equations

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.

A new fourth-order iterative method for finding multiple roots of nonlinear equations

In th is paper, we present a fifth-order method for find ing mult iple zeros of nonlinear equations. Per iteration, the new method requires two evaluations of functions and two of its first derivative. It is proved that the method has a convergence of order five. Finally, some numerical examples are g iven to show the performance of the presented method, and compared with some known methods.

A Third Order Iterative Method for Finding Zeros of Nonlinear Equations

‎In this paper‎, ‎we present a new modification of Newton's method‎ ‎for finding a simple root of a nonlinear equation‎. ‎It has been‎ ‎proved that the new method converges cubically‎.

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