The index of general nonlinear DAEs. (English) Zbl 0844.34007

Campbell, Stephen L.; Gear, C. William

Numer. Math. 72, No. 2, 173-196 (1995).

General nonlinear differential-algebraic equations (DAEs) are considered. For the characterization of the properties a lot of different index definitions are used in literature.
A (uniform \(k\)-)solvable DAE is introduced by considering a specially perturbed DAE. For solvable DAEs, a uniform and uniform differentiation index is defined and the relations to the classical differentiation and perturbation index are shown. By examples it is illustrated that the value of many of the different standard indices can vary widely. New maximum perturbation and differentiation indices which are more closely related, are introduced.

Reviewer: R.Lamour (Berlin)

MSC:

34A09	Implicit ordinary differential equations, differential-algebraic equations
65L99	Numerical methods for ordinary differential equations

Keywords:

nonlinear differential-algebraic equations; DAE; uniform differentiation index