On modelling and differential/algebraic systems

Abstract

It is of a vital interest that software for model development and simulation supports models given as differential/algebraic equa tions (DAE), since many models for physical systems are naturally given as sets of ordinary differential and algebraic equations and since, as motivated in the report, the equation form is the only reasonable for model libraries. Unfortunately, most simulation packages of today do not allow models given as DAE systems, but require assignment statements for derivatives and algebraic variables. There are numerical solvers for DAE systems, but they are not as reliable and robust as numerical solvers for ordinary differential equations on state space form. Unfortunately, DAE systems may exhibit bad properties, which make them difficult to solve numerically today. The purpose of the paper is to give an over view of important properties of DAE systems, indicate possible ways to handle difficulties and to motivate others to do research in this area. By means of examples it is illustrated that even small, simple DAE systems can exhibit bad properties. The examples are by no means pathological. They arise naturally during model development. There are many open questions to answer. The questions cover a broad range from theoretical to practical problems. To en courage research in this area, interesting issues are listed.