General Linear Methods for nonlinear DAEs in Circuit Simulation

Steffen Voigtmann

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 8

MSC 2000

65L80 Methods for differential-algebraic equations

34A09 Implicit equations, differential-algebraic equations

Abstract
The Modified Nodal Analysis leads to differential algebraic equations with properly stated leading terms. In this article a special structure of the DAEs modelling electrical circuits is exploited in order to derive a new decoupling for nonlinear index-2 DAEs. This decoupling procedure leads to a solvability result and is also used to study general linear methods, a class of numerical schemes that covers both Runge-Kutta and linear multistep methods. Convergence for index-2 DAEs is proved.