Multiple shooting is a well-known technique for the numerical solution of boundary value problems for ordinary differential equations. In order to solve the boundary value problems one has to solve initial value problems defined in the subintervalls of a given grid of shooting points. To solve the corresponding system of nonlinear algebraic equations one usually works with a Netwon method where in each iteration step the Jacobian matrix is replaced by a difference approximation. In an earlier paper \textit{S. Bellavia}, \textit{M. G. Gasparo} and \textit{M. Macconi} [J. Comput. Appl. Math. 71, No. 1, 83-93 (1996; Zbl 0856.65057)]\ have presented a so-called switching method for solving the system of nonlinear equations. This hybrid algorithm, where a damped finite approximation Newton method is combined with a minimization technique, is a globally quadratically convergent method. Theoretical results about this method were presented in earlier papers. Here, the numerical performance on a large set of test problems is investigated. The results demonstrate the effectiveness of the described method.