Collocation methods or the computation of periodic solutions of delay differential equations

In this paper we investigate collocation methods for the computation of per iodic solutions of autonomous delay differential equations ( DDEs). Periodi c solutions are found by solving a periodic two-point boundary value proble m, which is an infinite-dimensional problem for DDEs, in contrast to the ca se of ordinary differential equations. We investigate three collocation met hods based on piecewise polynomials. We discuss computational issues and sh ow numerical orders of convergence using an extensive number of tests. We c ompare our numerical results with known theoretical convergence results for initial value problems for DDEs. In particular, we show how superconvergen ce at the mesh points can be lost or recovered depending on the DDE model u nder consideration and on the choice of collocation discretization. We end with a brief discussion of adaptive mesh selection.