Introduction of Ostrowski Homotopy Continuation Method for Solving Nonlinear Equations using Mathematica

Abstract

The solution to a nonlinear equation is found in this study by combining a classical and a powerful method. Basically, it is well known that the homotopy continuation method (HCM) is a powerful method that has been used for solving the problem of the classical method. A new approach is introduced in this study which is known as the Ostrowski Homotopy Continuation method (Ostrowski-HCM) with a purpose to overcome the divergence problem that arises from the classical Ostrowski’s method when a bad initial guess is used. To put it simply, when the derivative of a given function at the starting point is equal to zero, the problem arises. As a result, the division by zero renders the scheme invalid. In addition, a mathematical software, Mathematica 7.0, is used to implement the Ostrowski-HCM results. Thus, from the analysis of the results, it is proven that the Ostrowski-HCM is reliable and advantageous for solving the nonlinear equation.