Homotopía y continuación numérica en sistemas no lineales

Abstract

This article presents the general idea of a numerical method for solving nonlinear systems which is different from the traditional iterative numerical methods and is based on the concept of homotopy and numerical continuation. We prove that solving a nonlinear system of equations is equivalent to solve an initial value problem of the first order. We use the classic fourth order        Runge-Kutta method to numerically solve the initial value problem. Finally, we include some results on the implementation of the proposed numerical method.