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Preprint 42-2014

Analysis and Numerical Solution of Linear Delay Differential-Algebraic Equations

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Author(s) : Phi Ha , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 42-2014

MSC 2000

34A09 Implicit equations, differential-algebraic equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

Abstract :
The analysis and numerical solution of initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Characteristic properties of DDAEs are analyzed and the differences between causal and noncausal DDAEs are studied. The method of steps is analyzed and it is shown that it has to be modified for general DDAEs. % The classification of ordinary delay differential equations (DDEs) is generalized to DDAEs, and a numerical solution procedure for general retarded and neutral DDAEs is constructed. The properties of the algorithm are studied and the theoretical results are illustrated with a numerical example.

Keywords : Delay differential-algebraic equation, differential-algebraic equation, delay differential equations, method of steps, derivative array, classification of DDAEs

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