New Iterative Methods for the Solution of Nonlinear Equations

Abstract

The proposed study develops a new iterative techniques to solve highly nonlinear equations of the form . Two techniques are employed, one of which involves the second derivative and the other free from the second derivative. The Taylor series is used to expand the function by substituting some equations  to get the two algorithms. Furthermore, several examples of nonlinear equations are considered to get the numerical solutions through the derived algorithms. The proposed work is compared with some other iterative techniques like Newton’s Method (NM), Adomian Method (AM), Newton Raphson Method (NRM), Chebyshev’s method (CM), and Halley’s Method (HM). The obtained results are highly accurate, and the convergence is faster than the techniques mentioned. The results are presented in tabular form and discussed which validates the current work and shows the impact of this article.