Discrete Fourier Series Approximation to Periodic Solutions of Autonomous Delay Differential Equations

This paper describes the algorithmic details involved in developing high-order Fourier series representations for periodic solutions to autonomous delay differential equations. Although the final approximate Fourier coefficients are computed by way of a nonlinear minimization algorithm, the steps to set up the objective function are shown to involve a sequence of matrix-vector operations. By proper coordination, these operations can be made very efficient so that high-order approximations can be obtained easily. An example of the calculations is shown for a Van der Pol equation with unit delay.