Spectra of Discrete Multi-Splitting Waveform Relaxation Methods to Determining Periodic Solutions of Linear Differential-Algebraic Equations

摘要

This chapter proposed spectra of discrete multi-splitting waveform relaxation (DMSWR) method to determine the periodic solutions of linear differential-algebraic equations. Based on the spectral radius of the derived operator by decoupled process, we obtained some convergent conditions for DMSWR method. The DMSWR method is an acceleration technique of the periodic waveform relaxation. A numerical example in circuit simulation is provided to further confirm the theoretical analysis and also to show that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process.