  The Douglas-Rachford method has been employed successfully to solve many
kinds of non-convex feasibility problems. In particular, recent research has
shown surprising stability for the method when it is applied to finding the
intersections of hypersurfaces. Motivated by these discoveries, we reformulate
a second order boundary valued problem (BVP) as a feasibility problem where the
sets are hypersurfaces. We show that such a problem may always be reformulated
as a feasibility problem on no more than three sets and is well-suited to
parallelization. We explore the stability of the method by applying it to
several examples of BVPs, including cases where the traditional Newton's method
fails.
