Structural Analysis and Dummy Derivatives: Some Relations

Abstract

Differential algebraic equations (DAEs) appear frequently in applications involving equation based modeling, from robotics to chemical engineering. A common way of making a DAE amenable to numerical solution is by reducing the index to obtain a corresponding ordinary differential equations (ODE) and using an ODE solution method. The signature matrix method developed by Pryce does not rely on an index reduction step and instead solves the DAE directly via Taylor series. The chapter draws comparisons between these two different approaches and shows the signature matrix method is in some sense equivalent to the dummy derivative index reduction method developed by Mattsson and Söderlind. The ideas are illustrated via a DAE from Campbell and Griepentrog that models a robot arm. The authors acknowledge G. Tan and N. Nedialkov at McMaster University, Hamilton, Canada for their support in this chapter and the talk that accompanied it at AMMCS-2013.