Perturbation versus Differentiation Indices

Co-author(s): Marcus Hausdorf

Reference: Computer Algebra in Scientific Computing - CASC 2001, V.G. Ghanza, E.W. Mayr, E.V. Vorozhtsov (eds.), Springer-Verlag, Berlin 2001, pp. 323-337

Description: We show how the perturbation index of a differential algebraic equation can be estimated by the determinacy index of a perturbed equation. Although this fact is not new, we present it in such a way based on the formal theory that it can readily be extended to overdetermined systems of partial differential equations. This is rigorously proven for smooth solutions of linear overdetermined systems. The crucial tool for our analysis is the Cartan normal form of an involutive system allowing us to introduce the analogue of an underlying equation for partial differential systems.

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