Unification of sixth-order iterative methods

Some Fifth and Sixth Order Iterative Methods for Solving Nonlinear Equations

In this paper, we derive multipoint iterative methods of fifth and sixth order for finding simple zeros of nonlinear equations. The methods are based on the composition of two steps – the first step consists of Jarratt fourth order method and the second is weighted Newton step to which correction term is applied. Per iteration each method requires two evaluations of the given function and two e...

Three-Step Iterative Methods with Sixth-Order Convergence for Solving Nonlinear Equations

In this paper, we develop new families of sixth-order methods for solving simple zeros of non-linear equations. These methods are constructed such that the convergence is of order six. Each member of the families requires two evaluations of the given function and two of its derivative per iteration. These methods have more advantages than Newton’s method and other methods with the same converge...

Efficiency of 2-order iterative methods

In this article the problem of solving a system of singular nonlinear equations will be discussed. New the iterative 2-order method for this problem is presented. The article includes the numerical results for the method. 1. Problem Let : n n F D R R ⊂ → be a nonlinear operator, D is an open set. The point 0 x D ∈ is given. The problem of solving a system of nonlinear equations consists in find...

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.