Charge-oriented extrapolation methods in digital circuit simulation (Q1902068)

The authors propose some extrapolation methods based on the linearly-implicit Euler scheme for numerical solving an initial value problem proceeding from the network equations of digital circuits derived charge-oriented modeling. To be compatible with the data structure used in CAD-based simulation packages for the transient analysis of electrical circuits, numerical integration software must be based on the charge-oriented formulation of the network equations. The extrapolation method with an unperturbed asymptotic expansion given here is based on the extrapolation algorithm proposed by \textit{W. B. Gragg} [J. Soc. Ind. Appl. Math., Ser. B, Numer. Anal. 2, 384-403 (1965; Zbl 0135.37803)]. The modified approach seems to be superior due to its better asymptotic expansion. The authors offer an industrial application ``the 8-bitcounter'' serving as an instructive real-life test problem.