The Waveform Relaxation Method for Systems of Differential/Algebraic Equations

An extension of the waveform relaxation (WR) algorithm to systems of differential/algebraic equations (DAE) is presented. Although this type of application has been explored earlier in relation to VLSI circuits, the algorithm has not been generalized to include the vast array of DAE system structures. The solvability and convergence requirements of the WR algorithm for higher-index systems are established. Many systems in robotics and control applications are modeled with DAE systems having an index greater than two. Computer simulation of these systems has been hampered by numerical integration methods which perform poorly and must be explicitly tailored to the system. The WR algorithm presents a means by which these systems may be more efficiently simulated by breaking them into weakly coupled subsystems, many of which will no longer retain the limiting high-index properties