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.
- Design Engineering Division and Computers and Information in Engineering Division
Discrete Fourier Series Approximation to Periodic Solutions of Autonomous Delay Differential Equations
- Views Icon Views
- Share Icon Share
- Search Site
Gilsinn, DE. "Discrete Fourier Series Approximation to Periodic Solutions of Autonomous Delay Differential Equations." Proceedings of the ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C. Long Beach, California, USA. September 24–28, 2005. pp. 719-728. ASME. https://doi.org/10.1115/DETC2005-84038
Download citation file: