Halley Irrational-Homotopy Analysis Method

Abstract

In this paper we investigate Halley irrational-homotopy analysis method as a new technique to find approximate solution of nonlinear equations, where complex and real roots are founded and in many cases we have two solutions. The Halleys irrational formula developed to determine the auxiliary (arbitrary) parameter in HAM. Furthermore, we also discuss in detail the order of convergence of this method. In order to validated and substantiate the performance of our contributed scheme, we give some examples.