third-order and fourth-order iterative methods free from second derivative 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.    

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

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...

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

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

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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.