Periodic waveform relaxation of nonlinear dynamic systems by quasi-linearization

In this brief, we provide an algorithm to treat periodic problems of nonlinear dynamic systems. Our approach is to apply quasi-linearization and waveform relaxation to a system of equations so as to produce a series of linear time-varying systems with periodicity constraints. We prove convergence of the algorithm and apply it to solutions of forced van der Pol equations as a further illustration.