The asymptotic behaviour of solutions of DAEs is determined by the flow restricted to certain constraints. Integration methods like the BDF method and the Runge-Kutta methods can produce numerical solutions with an entirely other asymptotic behaviour as expected from the ODE point of view. If the constraints and the corresponding subspaces, respectively, vary with respect to the time then integration methods have problems to reproduce these varations correctly. This implies additional problems for the stepsize control of iteration methods.

Here, we investigate the special class of DAEs which arises from the modified nodal analysis (MNA) in circuit simulation. We derive simple characterizations of the relevant subspaces. This allows us to present modelling criteria which guarantee that the numerical solution reflects the same asymptotical behaviour as the exact solution if we use the BDF method or a stiffly accurate implicit Runge-Kutta method.

MINISIMPOSIUM SESSION: 13. Numerical methods for DAEs