Ball comparison for three optimal eight order methods under weak conditions

Abstract

We considered three optimal eighth order method for solving nonlinear equations. In earlier studies Taylors expansions and hypotheses reaching up to the eighth derivative are used to prove the convergence of these methods. These hypotheses restrict the applicability of the methods. In our study we use hypotheses on the first derivative. Numerical examples illustrating the theoretical results are also presented in this study. 2019, Babes-Bolyai University.