Application of projection algorithms to differential equations: boundary value problems

Authors

DOI:

https://doi.org/10.21914/anziamj.v61i0.12165

Keywords:

boundary value problem, Douglas–Rachford method, Newton’s method, hypersurface.

Abstract

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. doi:10.1017/S1446181118000391

Author Biographies

Bishnu Lamichhane, CARMA University of Newcastle

Priority Research Centre for Computer-Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, New South Wales, Australia.

Scott Boivin Lindstrom, CARMA University of Newcastle

Priority Research Centre for Computer-Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, New South Wales, Australia.

Brailey Sims, CARMA University of Newcastle.

Priority Research Centre for Computer-Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, New South Wales, Australia.

Published

2019-03-25

Issue

Vol. 61 (2019)

Section

Articles for Printed Issues