Periodic waveform Krylov subspace method of circuit systems by multiple shooting

A multiple shooting technique is presented for determining the periodic responses of a linear circuit system by waveform relaxation (WR). Two ways to compute the unknown multiple shooting points are also provided. The new WR approach, namely a Krylov subspace algorithm in function space for a periodic system, is an accelerating process of classic WR with multiple shooting. The waveform Krylov subspace algorithm can enlarge the convergence region of function iterations. Further, the multiple shooting technique can numerically solve a periodic problem with a long interval in parallel.