Waveform iteration and one-sided Lipschitz conditions

Introduction From the end of the 1980's waveform-iteration(relaxation)-based algorithms become an industrial standard for circuit simulation by use of parallel computers [LRSV82, VC85, WSV82, JZ91]. Often they are implemented without further mathematical investigations for the correctness of the results. The experience has shown that for a wide class of VLSI circuits the waveformiteration -based simulation gives a good performance and correct results but there are also examples for which they fail. To get a wider class of applications for the waveform iteration we need further investigations to improve the efficiency and robustness of the algorithm. One question is, how to control the stepsize, such that the iteration process converges. Another question is, how many iterations are necessary to get the correct waveform. The influence of the discretization stepsize on the speed of convergence has been discussed in several publications for fixed stepsizes and linear systems of O