Revisit of Ostrowski's Method and Two New Higher Order Methods for Solving Nonlinear Equation

Abstract

In this paper, we have obtained the Ostrowski's method in a different way and proposed two new methods of order seven and thirteen. The efficiency index of Ostrowsky's method is 1.587 and that of the seventh order method and thirteenth order method are respectively 1.626 and 1.670, which are better than Newton's method (1.414) and Ostrowsky's method. Also it is observed from the numerical illustrations, the proposed methods take less number of iterations than Newton's method. Few other methods are compared with the proposed two methods, where the number of iterations for those methods are either same or more than the presented methods. Some examples are given to illustrate the performance of the new methods.