This paper presents a collocation method with an iterative linear system solver to compute periodic solutions of a system of autonomous delay differential equations (DDEs). We show that the linearized collocation system is equivalent to a discretization of the linearized periodic boundary value problem (BVP). This linear BVP is solved using the Newton-Picard single shooting method ([Int. J. Bifurcation Chaos, 7 (1997), pp. 2547– 2560]). The Newton-Picard method combines a direct method in the subspace of the weakly stable and unstable modes with an iterative solver in the orthogonal complement. As a side effect, we also obtain good estimates for the dominant Floquet multipliers. We have implemented the method in the DDE-BIFTOOL environment to test our algorithm.

- Collocation method
- MusicBrainz Picard
- Newton
- Collocation
- Iterative method
- Newton's method
- Dynamic Data Exchange
- Shooting method
- Discretization
- Linear system
- Lagrange multiplier
- Algorithm
- Instability
- Autonomous car
- Solutions
- Unstable Medical Device Problem
- Direct method in the calculus of variations
- Bifurcation theory