The use of block elimination for the calculation of some types of singularities efficiently

We will consider the use of block elimination for the calculation of generalized turning and bifurcation points for two point B.V.P.'s. It will be shown that such algorithm will reduce the amount of work required in terms of LU-factorizations to minimal. Since the discretization error of the approximated solution has an asymptotic expansion in terms of even powers of h (the step size). This will lead to the use of some type of extrapolation to produce more accurate results. Finite differences will be used to discretize the two point B.V.P's.