The study of parareal algorithm for the linear switched systems

We study in this paper the parareal (parallel-in-time) algorithm for the linear switched systems (LSS) on the basis of two coarse time subinterval divisions: the parareal algorithm based on the original switching time subinterval of the LSS (PLSS algorithm), and the parareal algorithm based on the new time subinterval division (NPLSS algorithm) for making the computation time of each processor well-balanced. These two proposed algorithms are able to compute the LSS with high-frequency oscillatory and discontinuous input efficiently. Besides, the convergence analysis of the two algorithms is provided.