Monotone waveform relaxation for systems of nonlinear differential-algebraic equations

We present a monotone waveform relaxation algorithm which produces very tig ht upper and lower bounds of the transient response of a class of systems d escribed by nonlinear differential-algebraic equations (DAEs) that satisfy certain Lipschitz conditions. The choice of initial iteration is critical a nd 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 l arger than previously reported. Numerical experiments are given to confirm the monotonicity of convergence of the algorithm.