Derivative free iterative methods with memory of arbitrary high convergence order

Abstract

In this article we present three derivative free iterative methods with memory to solve nonlinear equations. With the process developed, we can obtain n-step derivative free iterative methods with memory of arbitrary high order. Numerical examples are provided to show that the new methods have an equal or superior performance, on smooth and nonsmooth equations, compared to classical iterative methods as Steffensen's and Newton's methods and other derivative free methods with and without memory with high order of convergence.