Computational fixed point theory for differential delay equations with multiple time lags

We introduce a general computational fixed point method to prove existence of periodic solutions of differential delay equations with multiple time lags. The idea of such a method is to compute numerical approximations of periodic solutions using Newton's method applied on a finite dimensional projection, to derive a set of analytic estimates to bound the truncation error term and finally to use this explicit information to verify computationally  the hypotheses of the Banach fixed point theorem in a given Banach space. The yielded fixed point provide us the wanted periodic solution. We provide two applications. The first one is a proof of coexistence of three periodic solutions for a given delay equation with two time lags. The second application provides a rigorous computations of several nontrivial periodic solutions for a delay equation with three time lags.

The following links provide the programs sufficient to carry out the main result of the above mentioned work.