A waveform relaxation approach to determining periodic responses of linear differential-algebraic equations

We propose an algorithm, which is based on the waveform relaxation (WR) approach, to find the periodic responses of differential-algebraic equations. We derive an analytic expression of the spectral radius for the WR operator under a periodic constraint. Convergent splittings are obtained from this expression. Discrete waveforms are computed by the finite difference method. Numerical examples further illustrate the theoretical work in this paper.