New Iterative Methods for Solving Nonlinear Equations and Their Basins of Attraction

Abstract

The purpose of this paper is to propose new modified Newton's method for solving nonlinear equations and free from second derivative. Convergence results show that the order of convergence is four. Several numerical examples are given to illustrate that the new iterative algorithms are effective. In the end, we present the basins of attraction to observe the fractal behavior and dynamical aspects of the proposed algorithms.