Volume 25 , Issue 2 , December 2023 , Pages 1-9
1 Computer Department, College of Sciences, University of Salahaddin, Erbil, Kurdistan Region, Iraq
In the present article, we have constructed and looked at improving two- and three-step
iterative methods to locate simple roots of non-linear equations. It appears that the
three-step iterative method converges to the eighth order. The whole aim of this
research is to derive and present a new modified iterative method of higher order and to
obtain less iteration than the classical Newton method for solving nonlinear equations of
simple roots. The present technique has to evaluate three functions and two first
derivatives in each iteration. The advantage of the proposed method has been observed
to have at least better performance effective and more stability by comparing with the
other methods for the same or less than order. Also, noted that our method gives better
results in terms of the number of iterations. To demonstrate the efficacy and popularity,
different numerical illustrations are provided for the recommended techniques.