Simulating digital circuits numerically -- a charge-oriented ROW approach (Q1392763)

The author studies the numerical integration of a special class of differential algebraic equations arising in a charge-oriented approach to the simulation of digital networks. Under certain assumptions this class consists of index-2 systems of the special form \(A\dot q(x)-f(x)=0\) where \(A\) is an incidence matrix and \(q(x)\) the \(m\) terminal charges as functions of the \(n\) unknown node potentials \(x(t)\). The author shows that such systems can be solved by Rosenbrock-Wanner (ROW) methods for semi-explicit index-1 systems without order reduction. He introduces an embedded method of order (2)3 called CHORAL which uses projections to preserve the charge conservation. Its performance is demonstrated at two examples: a NAND gate and a two-bit adding unit. Compared with DASSL and various RODAS variants the new method needs less function evaluations to achieve a given precision.