SBA splitting for approximation of invariants in time-dependent Hamiltonian systems |
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Authors: | Fasma Diele Stefania Ragni |
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Affiliation: | a Istituto per le Applicazioni del Calcolo M. Picone, CNR, Via Amendola 122, 70126 Bari, Italy b Facoltà di Economia, Università di Bari, Via Camillo Rosalba 56, 70100 Bari, Italy |
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Abstract: | Most physical phenomena are described by time-dependent Hamiltonian systems with qualitative features that should be preserved by numerical integrators used for approximating their dynamics. The initial energy of the system together with the energy added or subtracted by the outside forces, represent a conserved quantity of the motion. For a class of time-dependent Hamiltonian systems [8] this invariant can be defined by means of an auxiliary function whose dynamics has to be integrated simultaneously with the system’s equations. We propose splitting procedures featured by a SB3A property that allows to construct composition methods with a reduced number of determining order equations and to provide the same high accuracy for both the dynamics and the preservation of the invariant quantity. |
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Keywords: | Time-dependent Hamiltonian systems Invariants Splitting and composition methods |
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