Steffen Schulz
Preprint series:
Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 15
MSC 2000
- 34A09 Implicit equations, differential-algebraic equations
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65L80 Methods for differential-algebraic equations
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65L06 Multistep, Runge-Kutta and extrapolation methods
Abstract
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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