The solution of non-linear sets of algebraic equations is usually obtained by the Newton's method, exhibiting quadratic convergence. For practical simulations, a significant computational effort consists in the evaluation of the Jacobian matrices. In this paper, we propose and experiment various methods to speed the convergence process either by re-using information from previous iterates or by by-passing the Jacobian evaluations. These methods are applied to the solution of hyperbolic PDE's arising in CFD problems. A significant improvement is obtained in terms of computation cost compared to the crude Newton's approach.