Fourth-order and fifth-order iterative methods for nonlinear algebraic 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.    

Fifth-order iterative methods for solving nonlinear equations

In this paper, we suggest and analyze a new two-step iterative method for solving nonlinear equation f(x) = 0 by rewriting the given nonlinear equation as a coupled system of equations and using the Taylor series. It is shown that this new iterative method is of fifth-order. Several examples are given to illustrate its performance and efficiency. Comparison with other methods is also given. Thi...

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

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.