Linear multistep methods for integrating reversible differential equations

Astronomical Journal

Volumn 118, Issue 4, 1999, Pages 1888-1899

  Evans, N Wyn ^a   Tremaine, Scott ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b PRINCETON UNIVERSITY OBSERVATORY   (United States)

Author keywords

Celestial mechanics, stellar dynamics; Methods: numerical

Indexed keywords

EID: 0040426340     PISSN: 00046256     EISSN: None     Source Type: Journal    
DOI: 10.1086/301057     Document Type: Article

References (28)

1. Arnold, V. I. 1984, in Nonlinear and Turbulent Processes in Physics, ed. R. Z. Sagdeev (Chur: Harwood), 1161
2. Calvo, M. P., López-Marcos, M. A., & Sanz-Serna, J. M. 1998, Appl. Numer. Math., 28, 1
3. Cano, B. 1996, Ph.D. thesis, Univ. Valladolid
4. Cano, B., & Sanz-Serna, J. M. 1998, IMA J. Numer. Anal., 18, 57
5. Channell, P. J., & Scovel, J. C. 1990, Nonlinearity, 3, 231
6. Davies, P. C. W. 1974, The Physics of Time Asymmetry (Berkeley: Univ. California Press)
7. Fukushima, T. 1998, in Proc. 30th Symp. on Celestial Mechanics, ed. T. Fukushima, T. Itoh, T. Fyse, & H. Umehara (Kanagawa), 229
8. _. 1999, in IAU Colloq. 173, Evolution and Source Regions of Asteroids and Comets, ed. J. Svoren & E. M. Pittich (Tatranská Lomnica: Slovak Acad. Sci.), in press
9. Gautschi, W. 1961, Numer. Math., 3, 381
10. Gear, C. W. 1971, Numerical Initial Value Problems in Ordinary Differential Equations (Englewood Cliffs, NJ: Prentice-Hall)
11. Henrici, P. 1962, Discrete Variable Methods in Ordinary Differential Equations (New York : Wiley)
12. Hockney, R. W., & Eastwood J. W. 1981, Computer Simulation Using Particles (London: McGraw-Hill)
13. Huang, W., & Leimkuhler, B. 1997, SIAM J. Sci. Comput., 18, 239
14. Hut, P., Funato, Y., Kokubo, E., Makino, J., & McMillan, S. 1997, in ASP Conf. Ser. 123, Computational Astrophysics, ed. D. A. Clarke & M. J. West (San Francisco : ASP), 26
15. Hut, P., Makino, J., & McMillan, S. 1995, ApJ, 443, L93
16. Kang, F. 1986, J. Comput. Math., 4, 279
17. Lambert, J. D. 1973, Computational Methods in Ordinary Differential Equations (New York: Wiley)
18. Lambert, J. D., & Watson, I. A. 1976, J. Inst. Math. Applications, 18, 189
19. Marsden, J. E., Patrick, W. G., & Shadwick, W. F., eds. 1996, Integration Algorithms and Classical Mechanics (Fields Inst. Commun. 10) (Providence: Am. Math. Soc.)
20. Mikkola, S. 1997, Celest. Mech. Dyn. Astron., 67, 145
21. Moser, J. 1973, Stable and Random Motions in Dynamical Systems (Princeton: Princeton Univ. Press)
22. Quinlan, G. D. 1999, preprint (astro-ph/9901136)
23. Quinlan, G. D., & Tremaine, S. 1990, AJ, 100, 1694
24. Quinn, T., Katz, N., Stadel, J., & Lake, G. 1997, ApJ, submitted (astro-ph/9710043)
25. Ralston, A. & Rabinowitz P. 1978, A First Course in Numerical Analysis (2d ed.; New York : McGraw-Hill)
26. Roberts, J. A. G., & Quispel, G. R. W. 1992, Phys. Rep., 216, 63
27. Sanz-Serna, J. M., & Calvo, M. P. 1994, Numerical Hamiltonian Problems (London: Chapman & Hall).
28. Yoshida, H. 1993, Celest. Mech. Dyn. Astron., 56, 27