Optimal Families of Eighth-Order Convergent Iterative Methods for Solving Nonlinear Equations Based on Ostrowsk's Method

Abstract

Solving nonlinear equations is one of the most important problems in numerical analysis, and has a wide range of application in various aspects, as well as many branches of science, engineering, physics, computing, astronomy, finance, ... Generally, it is difficult to find the exact root of the nonlinear equations, and so iterative methods become the efficient way to obtain approximate solutions. Recently Kou et. al. presented a class of new variants of Ostrowski's method with order of convergence equals seven (OSM7) for solving simple roots of nonlinear equations proposed in [7]. Ostrowski's method (OSM7) has efficiency index equals to √7 4