language: en

Distributed parallel shooting for BVODEs

K.L. Chow and W.H. Enright
Department of Computer Science, University of Toronto
E-mail : chow@cs.toronto.edu and enright@cs.toronto.edu

Abstract Many important scientific problems can be formulated as systems of ordinary differential equations with two-point boundary value constraints (BVODE). Multiple shooting is one of the most widely used numerical techniques for solving BVODE problems. In this work, we present a new distributed parallel numerical algorithm for BVODEs which is based on multiple shooting. We investigate the numerical stability of this new distributed algorithm and identify difficulties that can arise. We propose a new parallel iterative refinement scheme to cope with some specific numerical difficulties identified in our investigation. Computational experience is presented to demonstrate the potential effectiveness of our approach.

Keywords: Distributed parallel algorithm, boundary value problems, multiple shooting

1 Introduction