A note on the convergence order of some recent methods for solving nonlinear equations

Abstract

In this paper we show that some of the methods presented in Neta et al. (2014) do not possess optimal eighth order of convergence. Such methods are especially those obtained by Hermite interpolation. One of the two methods based on Jarratt’s optimal fourth order method possesses the convergence of seventh order whereas the other possesses fourth order. The methods based on King’s and Ostrowski’s optimal fourth order methods have convergence order six. The theoretical results are also verified through numerical example.