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

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

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SCHROPP, Johannes, 2000. Geometric Properties of Runge-Kutta Discretizations for Index 2 Differential Algebraic Systems

@unpublished{Schropp2000Geome-712, title={Geometric Properties of Runge-Kutta Discretizations for Index 2 Differential Algebraic Systems}, year={2000}, author={Schropp, Johannes} }

Geometric Properties of Runge-Kutta Discretizations for Index 2 Differential Algebraic Systems terms-of-use Schropp, Johannes eng 2011-03-22T17:45:35Z 2011-03-22T17:45:35Z application/pdf We analyze Runge-Kutta discretizations applied to index 2 differential algebraic equations (DAE's). We compare the asymptotic features of the numerical and the exact solutions. It is shown that Runge-Kutta methods satisfying the first order constraint condition of the DAE reproduce the geometric properties of the continuous system correctly. The proof combines embedding techniques of index 2 differential algebraic equations and ordinary differential equations with some invariant manifolds results of Nipp, Stoffer [12]. The results support the favourable behavior of these Runge-Kutta methods applied to index 2 DAE's for t >= 0. 2000 Schropp, Johannes

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