Positivity characterization of nonlinear DAEs. Part I: A flow formular for linear and nonlinear DAEs using projections

Abstract

We present a closed solution formula for differential-algebraic equations (DAEs) that generalizes the concept of the flow to linear and nonlinear problems of arbitrary index. This flow is stated in the original coordinate system and thus allows to study coordinate depending properties like positivity, in particular. Embedded in the concept of the strangeness-index, we separate the differential and algebraic components by a projection approach and remodel a given DAE as a semi-explicit system. Exploiting the results found in [2], we solve this system and compute a closed solution formula. Verifying that this solution is unique defined by the original DAE and uniquely related with a given consistent initial values, we construct the flow associated with a DAE with regular strangeness-index.