New Fourth Order Iterative Methods Second Derivative Free

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.

On optimal fourth-order iterative methods free from second derivative and their dynamics

In this paper new fourth order optimal root-finding methods for solving nonlinear equations are proposed. The classical Jarratt’s family of fourth-order methods are obtained as special cases. We then present results which describe the conjugacy classes and dynamics of the presented optimal method for complex polynomials of degree two and three. The basins of attraction of existing optimal metho...

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

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence