New families of symplectic splitting methods for numerical integration in dynamical astronomy
View/ Open
Impact
Scholar |
Other documents of the author: Blanes, Sergio; Casas, Fernando; Farrés Basiana, Ariadna; Laskar, Jacques; Makazaga, Joseba; Murua, Ander
Metadata
Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
New families of symplectic splitting methods for numerical integration in dynamical astronomyAuthor (s)
Date
2013-06Publisher
ElsevierBibliographic citation
BLANES, S.; CASAS PÉREZ, F.; FARRÉS BASIANA, A.; LASKAR, J.; MAKAZAGA, J.; MURUA, A. New families of symplectic splitting methods for numerical integration in dynamical astronomy. Applied Numerical Mathematics, Volume 68 (June 2013), Pages 58–72Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0168927413000135Version
info:eu-repo/semantics/publishedVersionAbstract
We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interested in very accurate results over a ... [+]
We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interested in very accurate results over a large time span. We derive in a systematic way an independent set of necessary and sufficient conditions to be satisfied by the coefficients of splitting methods to achieve a prescribed order of accuracy. Splitting methods satisfying such (generalized) order conditions are appropriate in particular for the numerical simulation of the Solar System described in Jacobi coordinates. We show that, when using Poincaré Heliocentric coordinates, the same order of accuracy may be obtained by imposing an additional polynomial equation on the coefficients of the splitting method. We construct several splitting methods appropriate for each of the two sets of coordinates by solving the corresponding systems of polynomial equations and finding the optimal solutions. The experiments reported here indicate that the efficiency of our new schemes is clearly superior to previous integrators when high accuracy is required [-]
Is part of
Applied Numerical Mathematics, Volume 68 (June 2013)Rights
http://rightsstatements.org/vocab/CNE/1.0/
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess
This item appears in the folowing collection(s)
- MAT_Articles [770]