Preservation of adiabatic invariants under symplectic discretization

Applied Numerical Mathematics

Volumn 29, Issue 1, 1999, Pages 45-55

  Reich, Sebastian ^a  

^a ZUSE INSTITUTE BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; INVARIANCE; MOLECULAR PHYSICS; NUMERICAL METHODS;

ADIABATIC INVARIANTS; HAMILTONIAN SYSTEMS; SYMPLECTIC DISCRETIZATION;

INTEGRATION;

EID: 0032755864     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(98)00032-4     Document Type: Article

References (15)

1. V.I. Arnold, V.V. Kozlov and A.I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics, 2nd ed. (Springer, New York, 1997).
2. U. Ascher and S. Reich, The midpoint scheme and variants for Hamiltonian systems: advantages and pitfalls, SIAM J. Sci. Comput., to appear.
3. O. Baldan and G. Benettin, Classical "freezing" of fast rotations: numerical test of the Boltzmann-Jeans conjecture, J. Statist. Phys. 62 (1991) 201.
4. G. Benettin, L. Galgani and A. Giorgilli, Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part I, Comm. Math. Phys. 113 (1987) 87-103.
5. G. Benettin and A. Giorgilli, On the Hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms, J. Statist. Phys. 74 (1994) 1117-1143.
6. F. Bornemann and Ch. Schütte, Homogenization of Hamiltonian systems with a strong constraining potential, Physica D 102 (1997) 57-77.
7. E. Hairer and Ch. Lubich, The life-span of backward error analysis for numerical integrators, Numer. Math. 76 (1997) 441-462.
8. M. Manziuk and T. Schlick, Resonance in the dynamics of chemical systems simulated by the implicitmidpoint scheme, Chem. Phys. Lett. 237 (1995) 525-535.
9. A.I. Neishtadt, The separation of motions in systems with rapidly rotating phase, J. Appl. Math. Mech. 48 (1984) 133-139.
10. S. Reich, Dynamical systems, numerical analysis, and exponentially small estimates, Habilitation Thesis, Berlin (1997).
11. H. Rubin and P. Ungar, Motion under a strong constraining force, Comm. Pure Appl. Math. 10 (1957) 65-87.
12. J.M. Sanz-Serna and M.P. Calvo, Numerical Hamiltonian Problems (Chapman and Hall, London, 1994).
13. R.D. Skeel, G. Zhang and T. Schlick, A family of symplectic integrators: stability, accuracy, and molecular dynamics applications, SIAM J. Sci. Comput. 18 (1997) 203-222.
14. F. Takens, Motion under the influence of a strong constraining force, in: Lecture Notes in Mathematics 819 (Springer, Berlin, 1980) 425-445.
15. L. Verlet, Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Phys. Rev. 159 (1967) 1029-1039.