In the present investigation we study the one{dimensional Saint{Venant equations_x000D_ (ESV) as a mathematical model for rectangular open channels with boundary_x000D_ conditions of the Dirichlet type and the implicit nite di erence scheme of_x000D_ Abbott{Ionescu which approximate the solutions of the (ESV). The convergence_x000D_ analysis of the approximate solutions is done by using the Equivalence Theorem of_x000D_ Lax{Richtmyer; that is, we analyze the consistency and stability of Abbott{Ionescu_x000D_ scheme