Three New Optimal Fourth-Order Iterative Methods to Solve Nonlinear Equations

Three New Optimal Fourth-Order Iterative Methods to Solve Nonlinear Equations

We present new modifications to Newton’s method for solving nonlinear equations. The analysis of convergence shows that these methods have fourth-order convergence. Each of the three methods uses three functional evaluations. Thus, according to KungTraub’s conjecture, these are optimal methods. With the previous ideas, we extend the analysis to functions with multiple roots. Several numerical e...

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.    

A new optimal method of fourth-order convergence for solving nonlinear equations

In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate,...

A Class of Iterative Methods for Solving Nonlinear Equations with Optimal Fourth-order Convergence

In this paper we construct a new third-order iterative method for solving nonlinear equations for simple roots by using inverse function theorem. After that a class of optimal fourth-order methods by using one function and two first derivative evaluations per full cycle is given which is obtained by improving the existing third-order method with help of weight function. Some physical examples a...