## Differential-algebraic systems as differential equations on manifolds

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- by Werner C. Rheinboldt PDF
- Math. Comp.
**43**(1984), 473-482 Request permission

## Abstract:

Based on the theory of differential equations on manifolds, existence and uniqueness results are proved for a class of mixed systems of differential and algebraic equations as they occur in various applications. Both the autonomous and nonautonomous case are considered. Moreover, a class of algebraically incomplete systems is introduced for which existence and uniqueness results only hold on certain lower-dimensional manifolds. This class includes systems for which the application of ODE-solvers is known to lead to difficulties. Finally, some solution approach based on continuation techniques is outlined.## References

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## Additional Information

- © Copyright 1984 American Mathematical Society
- Journal: Math. Comp.
**43**(1984), 473-482 - MSC: Primary 58F99; Secondary 34A15, 65L99
- DOI: https://doi.org/10.1090/S0025-5718-1984-0758195-5
- MathSciNet review: 758195