Application of projection algorithms to differential equations: boundary value problems
Numerical Analysis
2018-09-21 v3 Classical Analysis and ODEs
Optimization and Control
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.
Cite
@article{arxiv.1705.11032,
title = {Application of projection algorithms to differential equations: boundary value problems},
author = {Bishnu P. Lamichhane and Scott B. Lindstrom and Brailey Sims},
journal= {arXiv preprint arXiv:1705.11032},
year = {2018}
}