On the numerical solution of involutive ordinary differential systems : enhanced linear algebra

We analyse some Runge-Kutta type methods for computing 1D integral manifolds, i.e. solutions to ordinary differential equations and differential-algebraic equations. We show that we can compute the solutions which respect all the constraints of the problem reliably and reasonably quickly. Moreover, we show that the so-called impasse points are regular points in our approach and hence require no special attention