Computation and Bifurcation Analysis of Periodic Solutions of Large-scale Systems

This paper deals with the e cient computation and bifurcation analysis of periodic solutions of large-scale dynamical systems, such as systems arising from the spatial discretization of partial di erential equations. The Newton-Picard method is an e cient single-shooting based technique based on a Newton-like linearization which exploits the low-dimensional dynamics observed in many systems. The dominant, stabilitydetermining Floquet multipliers are easily recovered from the computations. In this paper, we develop an algebraic framework which generalizes older variants of the NewtonPicard method (including the Recursive Projection method) and which allows us to explain and to monitor the convergence behavior. Special attention is paid to algorithmic aspects which improve the robustness of the method. The e ciency of the approach is illustrated by some numerical results.