Differential-algebraic systems as differential equations on manifolds

Author:
Werner C. Rheinboldt

Journal:
Math. Comp. **43** (1984), 473-482

MSC:
Primary 58F99; Secondary 34A15, 65L99

MathSciNet review:
758195

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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.

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DOI:
https://doi.org/10.1090/S0025-5718-1984-0758195-5

Article copyright:
© Copyright 1984
American Mathematical Society