Numerical Method-Independent Structural Solvability Analysis of DAE Models

Abstract

A graph-theoretical method for the structural analysis of dynamic lumped process models described by differential and algebraic equations (DAEs) is applied in this paper in order to determine the most important solvability properties of these models by using the so-called dynamic representation graph. The construction of the dynamic representation graphs that was originally proposed for the most simple, single-step, explicit numerical methods, has been extended in this paper to higher order explicit and implicit solution methods, that are used more frequently and efficiently for numerical solution of DAE-systems. It is shown here that the representation graph for both higher order explicit and implicit solution methods has similar properties to the case of explicit numerical solution procedures both for index one and higher index models. Thus it is proven that the important properties of the representation graph including the differential index of the models are independent of the assumption whether a single-step, explicit or implicit numerical method is used for the solution of the differential equations.