Analysis of descriptor systems using numerical algorithms

In this paper we analyze numerical methods for the solution of the large scale dynamical system
E\dot{y}(t)=Ay(t)+g(t),Y(t_{0})=y_{0}
, where
E
and
A
are matrices, possibly singular. Systems of this type have been referred to as implicit systems and more recently as descriptor systems since they arise from formulating system equations in physical variables. Special cases of such systems are algebraic-differential systems. We discuss the numerical advantages of this formulation and identify a class of numerical integration algorithms which have accuracy and stability properties appropriate to descriptor systems and which preserve structure, detect nonsolvable systems, resolve initial value consistency problems, and are applicable to "stiff" descriptor systems. We also present an algorithm for the control of the local truncation error on only the state variables.