Articles

Optimized fifth order symplectic integrators for orbital problems

Kostas Tselios¹ and T. E. Simos^1,2

¹ Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR–221 00 Tripolis, Greece.

² Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia and Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and Technology, University of Peloponnese, GR–221 00 Tripolis, Greece. (tsimos.conf@gmail.com). Please use the following address for all correspondence: Dr. T. E. Simons, 10 Konitsis Street, Amfithea - Paleon Faliron, GR-175 64 Athens, Greece.

Received 2012 June 27.
Accepted 2012 September 3.

RESUMEN

Se presenta un integrador simpléctico optimizado de quinto orden. El desarrollo de este nuevo esquema se basa en: (1) un nuevo conjunto de condiciones para los esquemas simplécticos de paso k hasta de quinto orden, y (2) el error mínimo. Los resultados numéricos muestran la eficiencia del método propuesto.

ABSTRACT

In this paper an optimized fifth algebraic order symplectic integrator is produced. The development of the new scheme is based: (1) on a new set of conditions for symplectic k–step schemes with order up to five and (2) on the minimum error. The numerical results show the efficiency of the proposed method.

Key Words: methods: data analysis — methods: miscellaneous — methods: numerical.

DESCARGAR ARTÍCULO EN FORMATO PDF

REFERENCES

Candy, P. J., & Rozmus, W. 1991, J. Comp. Phys., 92, 230         [ Links ]

Forest, E. 2006, J. Phys. A: Math. Theoretical, 39, 5231         [ Links ]

Forest, E., & Ruth, R. D. 1990, Physica D, 43, 105         [ Links ]

Hairer, E., Lubich, C., & Wanner, G. 2002, Geometric Numerical Integration, Structure–Preserving Algorithms for Ordinary Differential Equations (Springer Series in Comput. Math., 31, Berlin: Springer–Verlag)         [ Links ]

Laskar, J., & Robutel, P. 2001, Celest. Mech., 80, 39         [ Links ]

Liu, X. S., Liu, X. Y., Zhou, Z. Y., Ding, P. Z., & Pan, S. F. 2000, Int. J. Quantum Chem., 79, 343        [ Links ]

McLachlan, R. I. 1995, BIT Numerical Math., 35, 258         [ Links ]

McLachlan, R. I., & Quispel, G. R. W 2006, J. Phys. A: Math. Theoretical, 39, 5251        [ Links ]

Nadolski, L., & Laskar, J. 2002, in 8th European Particle Accelerator Conference, ed. T. Garvey, L. Rivkin, J. Le Duff, C. Petit–Jean–Genaz, P. Le Roux, & J. Poole (Geneva: EPAC), 1276         [ Links ]

Omelyan, I. P., Mryglod, I. M., & Folk, R. 2002a, Phys. Rev. E, 65, 056706        [ Links ]

––––––––––. 2002b, Phys. Rev. E, 66, 026701        [ Links ]

Ruth, R. D. 1983, IEEE Trans. Nucl. Sci., NS–30, 2669         [ Links ]

Sanz–Serna, J. M., & Calvo, M. P. 1994, Numerical Hamiltonian Problem (London: Chapman & Hall)         [ Links ]

Tselios, K., & Simos, T. E. 2003, J. Math. Chem., 34(1), 83        [ Links ]

––––––––––. 2004, J. Math. Chem., 35(1), 55        [ Links ]

Yoshida, H. 1990, Phys. Lett., A, 150, 262         [ Links ]

––––––––––. 1993, Celest. Mech., 56, 27        [ Links ]