Geometric integration of Hamiltonian systems perturbed by Rayleigh damping |
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Authors: | Klas Modin Gustaf Söderlind |
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Institution: | (2) Mathematics Institute, University of Warwick, Warwick, UK; |
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Abstract: | Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed.
The dissipation is characterized by a small parameter ε, and the schemes under study preserve the symplectic structure in the case ε=0. In the case 0<ε≪1 the energy dissipation rate is shown to be asymptotically correct by backward error analysis. Theoretical results on monotone
decrease of the modified Hamiltonian function for small enough step sizes are given. Further, an analysis proving near conservation
of relative equilibria for small enough step sizes is conducted. |
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