On systems of nonlinear equations: some modified iteration formulas by the homotopy perturbation method with accelerated fourth- and fifth-order convergence

Variational iteration method and homotopy perturbation method for fourth-order fractional integro-differential equations

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

A third-order Newton type method for nonlinear equations based on modified homotopy perturbation method

In this paper, we present a new iterative method for solving nonlinear algebric equations by using modified homotopy perturbation method. We also discuss the convergence criteria of the present method. To assess its validity and accuracy, the method is applied to solve several test problems. 2007 Elsevier Inc. All rights reserved.

An Iterative Method with Fifth-Order Convergence for Nonlinear Equations

In this paper, we suggest and analyze a new four-step iterative method for solving nonlinear equations involving only first derivative of the function using a new decomposition technique which is due to Noor [11] and Noor and Noor [16]. We show that this new iterative method has fifth-order of convergence. Several numerical examples are given to illustrate the efficiency and performance of the ...

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,...