A Newton Type Iterative Method with Fourth-order Convergence

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

A modification of Newton method with third-order convergence

In this paper, we present a new modification of Newton method for solving non-linear equations. Analysis of convergence shows that the new method is cubically convergent. Per iteration the new method requires two evaluations of the function and one evaluation of its first derivative. Thus, the new method is preferable if the computational costs of the first derivative are equal or more than tho...

Convergence of Iterative Methods fora Fourth - Order Discretization

|We prove, that under certain conditions, some classical iterative methods converge for the linear system resulting from a fourth-order compact discretization of the convection-diiusion equation.

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 Modified Newton-Type Method with Sixth-Order Convergence for Solving Nonlinear Equations

In this paper, we present and analyze a sixth-order convergent method for solving nonlinear equations. The method is free from second derivatives and permits f'(x)=0 in some points. It requires three evaluations of the given function and two evaluations of its derivative in each step. Some numerical examples illustrate that the presented method is more efficient and performs better than classic...