Summary
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.
Zusammenfassung
Die Untersuchung der dynamischen Eigenschaften von Systemen mit Hilfe der mathematischen Prozeßsimulation geschieht häufig durch die Betrachtung des Systemverhaltens bei sprungartiger Veränderung der Eingangsgrößen (Sprung-Antwort-Verhalten). Eine genauere Analyse ([2]) zeigt, daß für Systeme in Form von Differential-Algebraischen Gleichungssystemen (sogar mit Index 1), welche häufig auftreten z.B. in der chemischen Verfahrenstechnik, eine Lösung dieser Aufgabe nicht existieren muß.
In dieser Arbeit leiten wir für Systeme vom Index 1 notwendige und hinreichende Bedingungen her, welche die Lösbarkeit des Problems garantieren (Theorem 1). Ferner wird ein einfacher Algorithmus zur numerischen Berechnung beschrieben (Theorem 3).
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References
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Brüll, L., Pallaske, U. On differential algebraic equations with discontinuities. Z. angew. Math. Phys. 43, 319–327 (1992). https://doi.org/10.1007/BF00946633
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DOI: https://doi.org/10.1007/BF00946633