Abstract: In this paper we consider the application of Quasi-Newton methods to the resolution of the Cavity Problem. This is a fourth order boundary value problem governed by the Navier-Stokes equations. Its finite difference discretization represents an interesting case study for algorithms that solve sparse nonlinear systems. We conclude that the Quasi-Newton algorithms that save on linear algebra at each iteration are more efficient than the classical Newton method. Key words: Nonlinear systems of equations, Newton's method, Quasi-Newton methods, stream function, Navier Stokes equations, cavity problems Ver menos