Abstract
<p style='text-indent:20px;'>In this paper we focus on the computation of periodic solutions of Delay Differential Equations (DDEs) with constant delays. The method is based on defining a Poincaré section in a suitable functional space and looking for a fixed point of the flow in this section. This is done by applying a Newton method on a suitable discretisation of the section. To avoid computing and storing large matrices we use a GMRES method to solve the linear system because in this case GMRES converges very fast due to the compactness of the flow of the DDE. The derivatives of the Poincaré map are obtained in a simple way, by applying Automatic Differentiation to the numerical integration. The stability of the periodic orbit is also obtained in a very efficient way by means of Arnoldi methods. The examples considered include temporal and spatial Poincaré sections.
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