Symmetric multistep methods over long times

Numerische Mathematik

Volumn 97, Issue 4, 2004, Pages 699-723

  Hairer, Ernst ^a   Lubich, Christian ^b  

^a UNIVERSITY OF GENEVA   (Switzerland)

^b UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3142580393     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-004-0520-2     Document Type: Article

References (19)

1. Benettin, G., Giorgilli, A.: On the Hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms. J. Statist. Phys. 74, 1117-1143 (1994)
2. Cano, B., Sanz-Serna, J. M.: Error growth in the numerical integration of periodic orbits by multistep methods with application to reversible systems. IMA J. Numer. Anal. 18, 57-75 (1998)
3. Dahlquist, G.: Stability and error bounds in the numerical integration of ordinary differential equations. Trans. of the Royal Inst. of Techn., Stockholm, Sweden 130, 1959
4. Evans, N. W., Tremaine, S.: Linear multistep methods for integrating reversible differential equations. Astron. J. 118, 1888-1899 (1999)
5. Fukushima, T.: Symmetric multistep methods revisited. In 30th Symposium on Celestial Mechanics, 1998, pp. 229-247
6. Fukushima, T.: Symmetric multistep methods revisited: II, Numerical experiments. In 173rd colloquium of the International Astronomical Union, 1999, pp. 309-314
7. Hairer, E.: Backward error analysis for multistep methods. Numer. Math. 84, 199-232 (1999)
8. Hairer, E., Hairer, M.: GniCodes - Matlab programs for geometric numerical integration. In: Frontiers in Numerical Analysis (Durham 2002), Springer, Berlin, 2003
9. Hairer, E., Leone, P.: Order barriers for symplectic multi-value methods. In: Numerical analysis 1997, Proc. of the 17th Dundee Biennial Conference 1997, D. F. Griffiths D. J. Higham & G. A. Watson eds. Pitman Research Notes in Mathematics Series. 380, 133-149 1998
10. Hairer, E., Lubich, C.: Long-time energy conservation of numerical methods for oscillatory differential equations. SIAM J. Numer. Anal. 38, 414-441 (2000)
11. Hairer, E., Lubich, C., Wanner, G.: Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations. Springer Series in Computational Mathematics 31. Springer, Berlin, 2002
12. Hairer, E., Lubich, C., Wanner, G.: Geometric numerical integration illustrated by the Störmer-Verlet method. Acta Numerica 12, 2003
13. Hairer, E., Nørsett, S. P., Wanner, G.: Solving Ordinary Differential Equations I. Non-stiff Problems. Springer Series in Computational Mathematics 8. Springer, Berlin, 2nd edition, 1993
14. Henrici, P.: Discrete Variable Methods in Ordinary Differential Equations. John Wiley & Sons Inc., New York, 1962
15. Lambert, J. D., Watson, I. A.: Symmetric multistep methods for periodic initial value problems. J. Inst. Maths. Applics. 18, 189-202 (1976)
16. Moser, J.: Stable and random motions in dynamical systems. Annals of Mathematics Studies. 77, 1973
17. Quinlan, G. D., Tremaine, S.: Symmetric multistep methods for the numerical integration of planetary orbits. Astron. J. 100, 1694-1700 (1990)
18. Störmer, C.: Sur les trajectoires des corpuscules électrisés. Arch. sci. phys. nat. Genève 24, 5-18, 113-158, 221-247 (1907)
19. Tang, Y.-F.: The symplecticity of multi-step methods. Computers Math. Applic. 25, 83-90 (1993)