Monotone Waveform Relaxation for Systems of Nonlinear Differential-Algebraic Equations

Abstract

We present a monotone waveform relaxation algorithm which produces very tight upper and lower bounds of the transient response of a class of systems described by nonlinear differential-algebraic equations (DAEs) that satisfy certain Lipschitz conditions. The choice of initial iteration is critical and we give two methods of finding it. We show that the class of systems in which monotone convergence of waveform relaxation is possible is actually larger than previously reported. Numerical experiments are given to confirm the monotonicity of convergence of the algorithm.