Geometric Properties of Runge-Kutta Discretizations for Nonautonomous Index 2 Differential Algebraic Systems

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2001
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Zusammenfassung

We analyze Runge-Kutta discretizations applied to nonautonomous index 2 differential algebraic equations (DAE's) in semi-explicit form. It is shown that for half-explicit and projected Runge-Kutta methods there is an attractive invariant manifold for the discrete system which is close to the invariant manifold of the DAE. The proof combines reduction techniques to autonomous index 2 differential algebraic equations with some invariant manifold results of Schropp. The results support the favourable behavior of these Runge-Kutta methods applied to index 2 DAE's for t >= 0.

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ISO 690SCHROPP, Johannes, 2001. Geometric Properties of Runge-Kutta Discretizations for Nonautonomous Index 2 Differential Algebraic Systems
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@unpublished{Schropp2001Geome-742,
  year={2001},
  title={Geometric Properties of Runge-Kutta Discretizations for Nonautonomous Index 2 Differential Algebraic Systems},
  author={Schropp, Johannes}
}
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