- Title
- Application of projection algorithms to differential equations: boundary value problems
- Creator
- Lamichhane, Bishnu P.; Lindstrom, Scott B.; Sims, Brailey
- Relation
- ANZIAM Journal Vol. 61, Issue 1, p. 23-46
- Publisher Link
- http://dx.doi.org/10.1017/S1446181118000391
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 2019
- Description
- The Douglas–Rachford method has been employed successfully to solve many kinds of nonconvex 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 value 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 BVPs, including cases where the traditional Newton’s method fails.
- Subject
- boundary value problem; Douglas–Rachford method; Newton’s method; hypersurface
- Identifier
- http://hdl.handle.net/1959.13/1400992
- Identifier
- uon:34850
- Identifier
- ISSN:1446-1811
- Rights
- © 2019 Australian Mathematical Society. This is a post-peer-review, pre-copyedit version of an article published in ANZIAM Journal. The final authenticated version is available online at http://dx.doi.org/10.1017/S1446181118000391
- Language
- eng
- Full Text
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