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Published online by Cambridge University Press:  18 February 2019

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


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.

Research Article
© 2019 Australian Mathematical Society 

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