| Title | Geometric integration of Hamiltonian systems perturbed by Rayleigh damping |
| Authors | Klas Modin, Gustaf Söderlind |
| Alternative Location | http://dx.doi.org/10.1007/s..., Restricted Access |
| Publication | Bit Numerical Mathematics |
| Year | 2011 |
| Volume | 51 |
| Issue | 4 |
| Pages | 977 - 1007 |
| Document type | Conference paper |
| Conference name | BIT50 Conference |
| Conference Date | Jun 17-20, 2010 |
| Conference Location | Lund, Sweden |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Springer |
| Abstract English | Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter epsilon, and the schemes under study preserve the symplectic structure in the case epsilon=0. In the case 0 <epsilon a parts per thousand(a)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. Numerical examples, verifying the analyses, are given for a planar pendulum and an elastic 3D pendulum. The results are superior in comparison with a conventional explicit Runge-Kutta method of the same order. |
| Keywords | Geometric numerical integration, Splitting methods, Weakly dissipative, systems, |
| ISBN/ISSN/Other | ISSN: 0006-3835 |
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