Computation of order conditions for symplectic partitioned Runge-Kutta schemes with application to optimal control
We derive order conditions for the discretization of (unconstrained) optimal control problems, when the scheme for the state equation is of Runge-Kutta type. This problem appears to be essentially the one of checking order conditions for symplectic partitioned Runge-Kutta schemes. We show that the c...
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Veröffentlicht in: | Numerische Mathematik 2006-03, Vol.103 (1), p.1-10 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We derive order conditions for the discretization of (unconstrained) optimal control problems, when the scheme for the state equation is of Runge-Kutta type. This problem appears to be essentially the one of checking order conditions for symplectic partitioned Runge-Kutta schemes. We show that the computations using bi-coloured trees are naturally expressed in this case in terms of oriented free tree. This gives a way to compute them by an appropriate computer program. |
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ISSN: | 0029-599X 0945-3245 |
DOI: | 10.1007/s00211-005-0661-y |