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We analyze the convergence of piecewise collocation methods for computingperiodic solutions of general retarded functional differential equations underthe abstract framework recently developed in [S. Maset, Numer. Math. (2016)133(3):525-555], [S. Maset, SIAM J. Numer. Anal. (2015) 53(6):2771--2793] and[S. Maset, SIAM J. Numer. Anal. (2015) 53(6):2794--2821]. We rigorously showthat a reformulation as a boundary value problem requires a properinfinite-dimensional boundary periodic condition in order to be amenable ofsuch analysis. In this regard, we also highlight the role of the period actingas an unknown parameter, which is critical since it is directly linked to thecourse of time. Finally, we prove that the finite element method is convergent,while we limit ourselves to commenting on the infeasibility of this approach asfar as the spectral element method is concerned.

Convergence analysis of collocation methods for computing periodic solutions of retarded functional differential equations