A further index concept for linear PDAEs of hyperbolic type

Abstract

For many technical systems the use of a refined network approach yields mathematical models given by initial-boundary value problems of partial differential algebraic equations (PDAEs). The boundary conditions of these systems are governed by time-dependent differential–algebraic equations (DAEs) that couple the PDAE system with the network elements that are modelled by DAEs in time only. As the numerical difficulties for a DAE can be classified by the index concept, it seems to be natural to generalize these ideas to the PDAE case. There already exist some approaches for parabolic and hyperbolic equations. Here, we will focus on a new kind of index, the characteristics index for hyperbolic equations, that does not depend on the elimination of one of the independent variables. It relies on the fact that hyperbolic PDEs can be regarded as ODEs along the characteristics.