Computing periodic solutions of linear differential equations by multi-splittings waveform relaxation

This paper use multi-splittings waveform relaxation (MSWR) method to determine the periodic solutions of linear differential equations. Based on the spectral radius of the derived operator by decoupled process, we obtain some convergent conditions for the MSWR method. The MSWR method is an acceleration technique of the periodic waveform relaxation. Numerical example 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.