Variable time step integration with symplectic methods

Applied Numerical Mathematics

Volumn 25, Issue 2-3, 1997, Pages 219-227

  Hairer, E ^a  

^a UNIVERSITY OF GENEVA   (Switzerland)

Author keywords

Backward error analysis; Hamiltonian systems; Kepler's problem; Symplectic integration; Variable step sizes; Verlet scheme

Indexed keywords

ALGORITHMS; ERROR ANALYSIS; INTEGRATION; MATHEMATICAL OPERATORS; NUMERICAL ANALYSIS; PERFORMANCE;

HAMILTONIANS;

DIFFERENTIAL EQUATIONS;

EID: 0031270028     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(97)00061-5     Document Type: Article

References (20)

1. M.P. Calvo and J.M. Sanz-Serna, The development of variable-step symplectic integrators, with application to the two-body problem, SIAM J. Sci. Comput. 14 (1993) 936-952.
2. B. Gladman, M. Duncan and J. Candy, Symplectic integrators for long-term integrations in celestial mechanics, Celestial Mech. Dynam. Astronomy 52 (1991) 221-240.
3. E. Hairer, Backward analysis of numerical integrators and symplectic methods, Ann. Numer. Math. 1 (1994) 107-132.
4. E. Hairer and C. Lubich, The life-span of backward error analysis for numerical integrators, Numer. Math. 16 (1997) 441-462.
5. E. Hairer and D. Stoffer, Reversible long-term integration with variable step sizes, SIAM J. Sci. Comput. 18 (1997) 257-269.
6. W. Huang and B. Leimkuhler, The adaptive Verlet method, SIAM J. Sci. Comput. 18 (1997) 239-256.
7. P. Hut, J. Makino and S. McMillan, Building a better leapfrog, Astrophys. J. 443 (1995) L93-L96.
8. T. Levi-Civita, Sur la résolution qualitative du problème restreint des trois corps, Acta Math. 30 (1906) 305-327.
9. T. Levi-Civita, Sur la régularisation du problème des trois corps, Acta Math. 42 (1920) 99-144.
10. R.I. McLachlan and C. Scovel, A survey of open problems in symplectic integration, Fields Inst. Commun. 10 (1996) 151-180.
11. R.J.Y. McLeod and J.M. Sanz-Serna, Geometrically derived difference formulae for the numerical integration of trajectory problems, IMA J. Numer. Anal. 2 (1982) 357-370.
12. S. Reich, Backward error analysis for numerical integrators, Preprint, Konrad-Zuse-Zentrum, Berlin (1996).
13. J.M. Sanz-Serna and M.P. Calvo, Numerical Hamiltonian Problems (Chapman and Hall, London, 1994).
14. R.D. Skeel and J.J. Biesiadecki, Symplectic integration with variable stepsize, Ann. Numer. Math. 1 (1994) 191-198.
15. R.D. Skeel and C.W. Gear, Does variable step size ruin a symplectic integrator? Phys. D 60 (1992) 311-313.
16. K.F. Sundman, Mémoire sur le problème des trois corps, Acta Math. 36 (1912) 105-179.
17. D. Stoffer, On reversible and canonical integration methods, Report 88-05, SAM, ETH Zürich (1988).
18. D. Stoffer, Variable steps for reversible integration methods, Computing 55 (1995) 1-22.
19. J. Waldvogel and F. Spirig, Chaotic motion in Hill's lunar problem, in: A.E. Roy and B.A. Steves, eds., From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, NATO Adv. Sci. Inst. Ser. B Phys. 336 (Plenum Press, New York, 1995).
20. K. Zare and V. Szebehely, Time transformations in the extended phase-space, Celestial Mechanics 11 (1975) 469-482.