Computable error bounds for approximate periodic solutions of autonomous delay differential equations

In this paper, we prove a result that says: Given an approximate solution and frequency to a periodic solution of an autonomous delay differential equation that satisfies a certain noncriticality condition, there is an exact periodic solution and frequency in a neighborhood of the approximate solution and frequency and, furthermore, numerical estimates of the size of the neighborhood are computed. Methods are outlined for estimating the parameters required to compute the errors. An application to a Van der Pol oscillator with delay in the nonlinear terms is given.