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Differential-algebraic systems as differential equations on manifolds. (English) Zbl 0581.65058
This paper develops existence and uniqueness results for a class of differential-algebraic equations (DAEs), both the autonomous and non- autonomous cases, based on the theory of differential equations on manifolds. It is also shown that certain DAEs are algebraically incomplete and possess existence and uniqueness properties only on certain lower dimensional manifolds. Algebraic incompleteness appears to be a main cause of difficulty when ODE solvers are applied to DAEs. As a consequence the author concludes by suggesting methods based on continuation techniques as being suitable for solving DAEs instead of those based on ODE techniques.
Reviewer: K.Burrage

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
37N99 Applications of dynamical systems
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