Numerical integration of differential algebraic systems and invariant manifolds
| Autor: | Nipp, Kaspar |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 1999 |
| Předmět: | |
| Zdroj: | SAM Research Report, 1999-12 |
| DOI: | 10.3929/ethz-a-004284985 |
| Popis: | The dynamics of a differential algebraic equation takes place on a lower dimensional manifold in phase space. Applying a numerical integration scheme, it is natural to ask if and how this geometric property is preserved by the discrete dynamical system. In the index-1 case answers to this question are obtained from the singularly perturbed case treated in [6] for Runge-Kutta methods and in [7] for linear multistep methods. As main result, it is shown that also for Runge-Kutta methods and linear multistep methods applied to an index-2 problem of Hessenberg form there is a (attractive) invariant manifold for the discrete dynamical system and this manifold is close to the manifold of the differential algebraic equation. SAM Research Report, 1999-12 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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