Index analysis of unsteady-state chemical process systems—I. An algorithm for problem formulation

Abstract The convergence properties of the numerical methods used for solving systems of differential/ algebraic equations (DAEs) depend upon a very important property of a DAE, its index. In general, index-one problems can be solved routinely, while higher-index problems may present difficulties or be practically unsolvable. The index of DAEs describing chemical processes is strongly affected by the precise formulation of the problem, that is, by the choice of independent variables and equations. Since these choices can often be made rather arbitrarily, it is important that the index be made a criterion in making this choice. In Part I of this set of two papers we present an algorithm for selecting, whenever possible, the independent equations and variables that lead to the formulation of an index-one DAE.