Symplectic variable step size integration for N-body problems

Applied Numerical Mathematics

Volumn 29, Issue 1, 1999, Pages 19-30

  Hardy, David J ^a   Okunbor, Daniel I ^b   Skeel, Robert D ^a  

^a University of Illinois at Urbana Champaign   (United States)

^b University of Missouri Rolla   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DIFFERENTIAL EQUATIONS; DYNAMICS; MOLECULAR PHYSICS; NUMERICAL METHODS; PROBLEM SOLVING;

HAMILTONIAN SYSTEMS; MULTIPLE TIME STEPPING; SYMPLECTIC INTEGRATION;

INTEGRATION;

EID: 0032737545     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(98)00031-2     Document Type: Article

References (22)

1. S.P. Auerbach and A. Friedman, Long-time behavior of numerically computed orbits: small and intermediate timestep analysis of one-dimensional systems, J. Comput. Phys. 93 (1991) 189-223.
2. M.P. Calvo and J.M. Sanz-Serna, The development of variable-step symplectic integrators, with applications to the two-body problem, SIAM J. Sci. Statist. Comput. 14 (1993) 936-952.
3. G.C. Fox, M.A. Johnson, G.A. Lyzenga, S.W. Otto, J.K. Salmon and D.W. Walker, Solving Problems on Concurrent Processors, Vol. I: General Techniques and Regular Problems (Prentice-Hall, Englewood Cliffs, NJ, 1988).
4. L. Greengard, The Rapid Evaluation of Potential Fields in Particle Systems (MIT Press, Cambridge, MA, 1988).
5. H. Grubmüller, H. Heller, A. Windemuth and K. Schulten, Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions, Molec. Sim. 6 (1991) 121-142.
6. E. Hairer, Variable time step integration with symplectic methods, Ann. Numer. Math. 1 (1994) 102-132.
7. D.J. Hardy, Multiple time step symplectic integration, Master's Thesis, University of Missouri-Rolla (1997).
8. D.J. Hardy and D.I. Okunbor, Symplectic multiple time step integration, J. Comput. Phys., submitted.
9. W. Huang and B. Leimkuhler, The adaptive Verlet method, SIAM J. Sci. Comput. 18 (1997) 239-256.
10. P. Hut, J. Makino and S. McMillan, Building a better leapfrog, Astrophys. J. 443 (1995) L93-L96.
11. M.H. Lee, M.J. Duncan and H.F. Levison, Variable timestep integrators for long-term orbital integrations, in: Computational Astrophysics, Proc. 12th Kingston Meeting (1997).
12. T.R. Littell, R.D. Skeel and M. Zhang, Error analysis of symplectic multiple time stepping, SIAM J. Numer. Anal. 34 (1997) 1762-1807.
13. R.I. McLachlan and C. Scovel, A survey of open problems in symplectic integration, in: J.E. Marsden, G.W. Patrick and W.F. Shadwick, eds., Integration Algorithms and Classical Mechanics (American Mathematical Society, Providence, RI, 1996).
14. D.I. Okunbor, Variable step size does not harm second-order integrators for Hamiltonian systems, J. Comput. Appl. Math. 47 (1993) 273-275.
15. S. Reich, Backward error analysis for numerical integrators, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Preprint SC 96-21 (1996).
16. J.M. Sanz-Serna and M.P. Calvo, Numerical Hamiltonian Problems (Chapman and Hall, London, 1994).
17. R.D. Skeel and J.J. Biesiadecki, Symplectic integration with variable stepsize, Ann. Numer. Math. 1 (1994) 191-198.
18. R.D. Skeel and C.W. Gear, Does variable step size ruin a symplectic integrator?, Physica D 60 (1992) 311-313.
19. W.B. Streett, D.J. Tildesley and G. Saville, Multiple time-step methods in molecular dynamics, Molec. Phys. 35 (1978) 639-648.
20. S. Toxvaerd, Hamiltonians for discrete dynamics, Phys. Rev. 50 (1994) 2271-2274.
21. M. Tuckerman, B.J. Berne and G.J. Martyna, Reversible multiple time scale molecular dynamics, J. Chem. Phys. 97 (1992) 1990-2001.
22. L. Verlet, Computer 'experiments' on classical fluids I. Thermodynamical properties of Lennard-Jones molecules, Phys. Rev. 159 (1967) 98-103.