An optimal 8th order Newton’s-type method with basin of attraction

Abstract

The goal of the present work is to obtain an eighth order optimal Newton like method to solve non-linear algebraic equations. We also examine the dynamics of the proposed method. It is an optimal eighth order consistent with Kung–Traub conjecture with efficiency index 1.682. We have tested the proposed method using several numerical examples and also discussed the basin of attraction related to some numerical examples. © 2021, The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada.