We propose a geometric approach for the numerical integration of singular
initial value problems for (systems of) quasi-linear differential equations. It
transforms the original problem into the problem of computing the unstable
manifold at a stationary point of an associated vector field and thus into one
which can be solved in an efficient and robust manner. Using the shooting
method, our approach also works well for boundary value problems. As examples,
we treat some (generalised) Lane-Emden equations and the Thomas-Fermi equation.Comment: 29 pages, 9 figure