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Global modified Hamiltonian for constrained symplectic integrators

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Published in Numerische Mathematik. 2003, vol. 95, no. 2, p. 325-336
Abstract We prove that the numerical solution of partitioned Runge-Kutta methods applied to constrained Hamiltonian systems (e.g., the Rattle algorithm or the Lobatto IIIA--IIIB pair) is formally equal to the exact solution of a constrained Hamiltonian system with a globally defined modified Hamiltonian. This property is essential for a better understanding of their longtime behaviour. As an illustration, the equations of motion of an unsymmetric top are solved using a parameterization with Euler parameters.
Keywords Constrained Hamiltonian systemsSymplectic integratorsPartitioned Runge-Kutta methodsGenerating functionsBackward error analysisModified Hamiltonian
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HAIRER, Ernst. Global modified Hamiltonian for constrained symplectic integrators. In: Numerische Mathematik, 2003, vol. 95, n° 2, p. 325-336. https://archive-ouverte.unige.ch/unige:12278

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Deposited on : 2010-11-01

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