Fifth and Eleventh-Order Iterative Methods for Roots of Nonlinear Equations

Abstract

In this work, two iterative methods, based on Newton’s method, to obtain the numerical solutions of nonlinear
equations have been constructed. We proved that our methods converge in fifth and eleventh orders. Analytical
investigation has been established to show that our schemes have higher efficiency indexes than some recent
methods. Numerical examples are experimented to investigate the performance of the proposed schemes. Moreover,
theoretical order of convergence is verified on the experiment work.