Derivative-Free Iterative Methods with Some Kurchatov-Type Accelerating Parameters for Solving Nonlinear Systems

Two Efficient Derivative-Free Iterative Methods for Solving Nonlinear Systems

In this work, two multi-step derivative-free iterative methods are presented for solving system of nonlinear equations. The new methods have high computational efficiency and low computational cost. The order of convergence of the new methods is proved by a development of an inverse first-order divided difference operator. The computational efficiency is compared with the existing methods. Nume...

A Note on Some Higher-Order Iterative Methods Free from Second Derivative for Solving Nonlinear Equations

In the recent paper [M. A. Noor, W. A. Khan, K. I. Noor and Eisa Al-Said, Higher-order iterative methods free from second derivative for solving nonlinear equations, International Journal of the Physical Sciences, Vol. 6 (8) (2011), 1887-1893] several iterative methods for solving nonlinear equations are presented. One of the methods is the three-step iterative method given in Algorithm (2.10) ...

Seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations

A Family of Optimal Derivative Free Iterative Methods with Eighth-Order Convergence for Solving Nonlinear Equations

In this paper, modification of Steffensen’s method with eight-order convergence is presented. We propose a family of optimal three-step methods with eight-order convergence for solving the simple roots of nonlinear equations by using the weight function and interpolation methods. Per iteration this method requires four evaluations of the function which implies that the efficiency index of the d...

seventh-order iterative algorithm free from second derivative for solving algebraic nonlinear equations