An Optimal Reconstruction of Chebyshev–Halley-Type Methods with Local Convergence Analysis

Abstract

Our principle aim in this paper is to present a new reconstruction of classical Chebyshev–Halley schemes having optimal fourth and eighth-order of convergence for all parameters [Formula: see text] unlike in the earlier studies. In addition, we analyze the local convergence of them by using hypotheses requiring the first-order derivative of the involved function [Formula: see text] and the Lipschitz conditions. In addition, we also formulate their theoretical radius of convergence. Several numerical examples originated from real life problems demonstrate that they are applicable to a broad range of scalar equations, where previous studies cannot be used. Finally, a dynamical study of them also demonstrates that bigger and more promising basins of attractions are obtained.