ODE Methods for the Solution of Differential/Algebraic Systems

In this paper we study the numerical solution of the differential/algebraic systems $F(t,y,y') = 0$. Many of these systems can be solved conveniently and economically using a range of ODE methods. Others can be solved only by a small subset of ODE methods, and still others present insurmountable difficulty for all current ODE methods. We examine the first two groups of problems and indicate which methods we believe to be best for them. Then we explore the properties of the third group which cause the methods to fail. We describe a reduction technique which allows systems to be reduced to ones that can be solved. It also provides a tool for the analytical study of the structure of systems.