The Consistent Initialization of Differential-Algebraic Systems

The initial values for Variables in mixed Differential-Algebraic (DAE) systems must satisfy not only the original equations in the system but also their differentials with respect to time. Whether or not this additional requirement actually imposes extra constraints on the initial Values depends on the particular problem. This paper derives a criterion for determining whether differentiation of a subset of the equations of a nonlinear DAE system provides further constraints to be satisfied by the initial values. A graph-theoretical algorithm is proposed to locate those subsets of the system equations which need to be differentiated.