Newton Homotopy Continuation Method for Solving Nonlinear Equations using Mathematica

Abstract

In this paper, we solve the nonlinear equations by using a classical method and a powerful method.  A powerful method known as homotopy continuation method (HCM) is used to solve the problem of classical method.  We use Newton-HCM to solve the divergence problem that the classical Newton’s method always faces. The divergence problem occurs when a bad initial guess is used. The problem with Newton’s method happens when the derivative of given function at initial point equal to zero. The division by zero makes the scheme become nonsense. Thus, an approach used to solve this mathematical problem by using Newton-HCM. The results are implemented by mathematical software known as Mathematica 7.0. The results obtained indicate the ability of Newton-HCM to solve this mathematical problem.