ON DIFFERENTIAL ALGEBRAIC EQUATIONS WITH DISCONTINUITIES

The dynamic features of systems in mathematical process simulation are often studied by looking at the response of the system to discontinuities in the input variables (Sprung-Antwort-Verhalten). A more detailed analysis ([2]) shows that for systems in the form of differential algebraic equations (even with index 1), which frequently occur e.g. in chemical engineering, a solution to the problem need not exist. In this paper we derive necessary and sufficient conditions for such systems to guarantee the solvability of the problem (Theorem 1). Further, a simple algorithm is stated (Theorem 3), which is suitable for numerical computation.