Photo by markuswinkler from unsplash
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… Click to show full abstract
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.
Journal Title: ANZIAM Journal
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!