Integration schemes for highly oscillatory DAEs with applications to circuit simulation

A new numerical integration scheme for the simulation of differential-algebraic equations is presented. In the context of the computer-aided design of electronic circuits, the modeling of highly oscillatory circuits leads to oscillatory differential-algebraic equations. Standard schemes can solve these equations neither efficiently nor reliably. To overcome the problems of classical numerical methods, the new discretization scheme is based on the principle of coherence due to Hersch in combination with a multistep approach. A Fortran77 implementation of the presented integration scheme reduces the simulation time for a quartz-controlled oscillator to about 2% compared with standard methods. Theretore, it is a useful tool for the design of highly oscillatory circuits.