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arXiv · 1705.11032

Application of projection algorithms to differential equations: boundary value problems

Bishnu P. Lamichhane·Scott B. Lindstrom·Brailey Sims
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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.

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Bishnu P. Lamichhane, Scott B. Lindstrom, Brailey Sims. 2017-05-31. Application of projection algorithms to differential equations: boundary value problems. https://arxiv.org/abs/1705.11032

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