Multi-splitting Waveform Relaxation Methods for Determining Periodic Solutions of Linear Differential-Algebraic Equations

This paper use multi-splittings waveform relaxation (MSWR) method to determine the periodic solutions of linear differential-algebraic equations. Based on the spectral radius of the derived operator by decoupled process, we obtain some convergent conditions for the MSWR method. Numerical example in circuit simulation is provided to further confirm the theoretical analysis and also show that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process.