New three step derivative free iterative method for solving nonlinear equations
Authors :
Najmuddin Ahmad 1 * and Vimal Pratap Singh 2
Author Address :
1,2 Department of Mathematics, Integral University, Lucknow-226026, Uttar Pradesh, India.
*Corresponding author.
Abstract :
In this paper, we present a three step derivative free iterative method for solving nonlinear equations $ f(x) = 0 $. We discuss the convergence criteria of this new derivative free iterative method. A comparison with other existing methods is also given. The aim of this paper is to develop a new derivative free iterative method to find the approximation of the root $\alpha$ is nonlinear equations $ f(x) = 0 $, without the evaluation of the derivatives. This new method is based on Steffensen's method [11]. It is prove that the new method has cubic convergence. The benefit of this method is that it does not need to calculate any derivative. Numerical comparisons are made with other existing methods to show the better performance of the presented method.
Keywords :
Nonlinear equations, convergence analysis, iterative methods, derivative free, three step.
DOI :
Article Info :
Received : March 19, 2020; Accepted : August 18, 2020.
