Computing in the past with forward integration

Using existing, forward-in-time integration schemes, we demonstrate that under certain conditions it is possible to compute the solution at earlier times, even in the presence of stiffness (for which reverse integration is unstable). This technique can be used when a reverse integrator is not available--for example, when all one has is a forward-in-time legacy code. It can also be used for the 'reverse coarse' integration of the macroscopic closure of a system defined by a microscopic model which itself is naturally forward in time (e.g., a particle model of a gas). The method proposed has stability properties that enable it to converge to stationary points of unstable stiff systems