Some variants of Cauchy's method with accelerated fourth-order convergence

Some variants of Cauchy’s method with accelerated fourth-order convergence

In this paper, we present some variants of Cauchy’s method for solving non-linear equations. Analysis of convergence shows that the methods have fourth-order convergence. Per iteration the new methods cost almost the same as Cauchy’s method. Numerical results show that the methods can compete with Cauchy’s method. © 2007 Published by Elsevier B.V. MSC: 41A25; 65D99

Certain improvements of Newton's method with fourth-order convergence

In this paper we present two new schemes, one is third-order and the other is fourth-order. These are improvements of second-order methods for solving nonlinear equations and are based on the method of undetermined coefficients. We show that the fourth-order method is more efficient than the fifth-order method due to Kou et al. [J. Kou, Y. Li, X. Wang, Some modifications of Newton’s method with...

Some fourth-order modifications of Newton's method

In this paper, we construct some fourth-order modifications of Newton’s method for solving nonlinear equations. Any two existing fourth-order methods can be effectively used to give rise to new fourth-order methods. Per iteration the new methods require two evaluations of the function and one of its first-derivative. Numerical examples are given to show 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,...

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