The index of general nonlinear DAEs
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.
nonlinear differential-algebraic equations
scientific article; zbMATH DE number 839154