A Newton-Picard algorithm for computing periodic solutions of large scale dynamical systems

Alastair Spence
School of Mathematical Sciences
University of Bath

Abstract: This talk is concerned with the efficient computation of periodic orbits in large-scale dynamical systems that arise after spatial discretization of PDEs. A hybrid Newton-Picard scheme based on the shooting method is derived, which in its simplest form is the Recursive Projection Method of Schroff and Keller, and is used to compute and determine the stability of both stable and unstable periodic orbits.