Computing Connecting Orbits via an Improved Algorithm for Continuing Invariant Subspaces

James Weldon Demmel, Luca Dieci, Mark J. Friedman

Abstract: A successive continuation method for locating connecting orbits in parametrized systems of autonomous ODEs was considered in [Numer. Algorithms, 14 (1997), pp. 103--124]. In this paper we present an improved algorithm for locating and continuing connecting orbits, which includes a new algorithm for the continuation of invariant subspaces. The latter algorithm is of independent interest and can be used in contexts different than the present one.