Two High Order Iterative Methods for Roots of Nonlinear Equations

Abstract

This study suggests new iterative methods, based on the conventional Newton’s method, to obtain the numerical solutions of nonlinear equations. We prove that our methods include five and ten orders of convergence. Also, the convergence behavior and comparison with an existing results of the proposed schemes are investigated. Numerical experiments demonstrate that the proposed schemes are able to attain up to the better accuracy than some classical methods, while still significantly reducing the total number of calculations and iterations.