Abstract
The numerical solution of systems of partial differential and algebraic equations (PDAEs) is strictly related to a property of the system, the index, whose definition and role are discussed in this paper. The notion of algebraic index is reviewed and compared to the more general notion of perturbation index. Extensions to nonlinear PDAEs are also proposed. Reference is then made to the case of a flexible mechanical system (an inextensible cable), whose model is formulated in three different, yet dynamically equivalent, ways, with different properties with respect to the feasibility of an accurate numerical integration. The methodology used in this analysis is finally formalized in an algorithm for index reduction.
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