Superconvergence and the computation of generalized turning points for B.V.P's

We consider projection methods in general and collocation at gauss points in particular for the numerical computation of generalized turning points for two point B.V.P's. We discretize the original problem using collocation to obtain a finite dimensional problem. We will employ a direct method for the characterization and computation of simple turning points. Proper extensions of this direct method will be used for the computation of bifurcation points and cubic turning points. We comment also on the superconvergence which will be clear from the numerical examples.