For linear differential-algebraic equations (DAEs) with properly
stated leading terms the property of being numerically qualified
guarantees that qualitative properties of DAE solutions are reflected
by the numerical approximations. In this case BDF and Runge-Kutta
methods integrate the inherent regular ODE.
Here, we extend these results to general linear methods. We show
how general linear methods having stiff accuracy can be applied to
linear DAEs of index 1 and 2. In addition to the order conditions for
ODEs, general linear methods for DAEs have to satisfy additional
conditions.
As general linear methods require a starting procedure to start the
integration we put special emphasis on finding suitable starting
methods for index-2 DAEs.