Formal Theory of Differential-algebraic Systems

1994 Abstract. We propose a new approach to diierential-algebraic systems based on the formal theory of partial diierential systems. This results in a new deenition of the index of the system, which is similar to but more general than the one proposed recently by Rabier and Rheinboldt. This index, however, is not related to the numerical diiculty of solving the system, but to the amount of symbolic computation required to transform the system into a formally integrable system. We argue that this latter concept is essential in the numerical treatment of the problem and suggest that any numerical method for general diierential-algebraic systems should be based on solving only formally integrable systems. This requires in general that one must be able to deal explicitly with overdetermined systems.