Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods

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...

Latus: A new accelerator for generating combined iterative methods in solving nonlinear equation

latus: a new accelerator for generating combined iterative methods in solving nonlinear equation

A new iterative with memory class for solving nonlinear ‎equations‎

In this work we develop a new optimal without memory class for approximating a simple root of a nonlinear equation. This class includes three parameters. Therefore, we try to derive some with memory methods so that the convergence order increases as high as possible. Some numerical examples are also ‎presented.‎‎

New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations

A new family of eighth-order derivative-freemethods for solving nonlinear equations is presented. It is proved that these methods have the convergence order of eight. These new methods are derivative-free and only use four evaluations of the function per iteration. In fact, we have obtained the optimal order of convergence which supports the Kung and Traub conjecture. Kung and Traub conjectured...