Analysis and numerical solution of linear delay differential-algebraic equations

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 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.