Symbolic Numeric Index Analysis Algorithm for Differential Algebraic Equations

Abstract

Mathematical modeling of dynamic chemical engineering systems such as flow-sheet simulation, transient analysis of reaction and separation networks, computational fluid dynamic, or control problems often leads to systems of differential−algebraic equations (DAEs). Knowing the index of a DAE is an important prerequisite for its consistent initialization and its numerical solution. For large sets of DAEs occurring in chemical engineering practice, index analysis requires computational procedures. This paper presents a new approach for automatic index analysis. Earlier index analysis algorithms were based on purely structural calculus. Unfortunately, structural methods may actually arbitrarily over- or underestimate the correct DAE index. To overcome the shortcomings of existing approaches, this paper proposes a novel algorithm expanding DAE analysis to include both symbolic and numerical information. The novel symbolic numerical analysis accounts for variable cancellation and processes linear expressions ac...