2005-11-03Buch DOI: 10.18452/2608
General linear methods for linear DAEs
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
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.
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