Free Access
Issue
ESAIM: M2AN
Volume 43, Number 4, July-August 2009
Special issue on Numerical ODEs today
Page(s) 631 - 644
DOI https://doi.org/10.1051/m2an/2009019
Published online 08 July 2009
  1. S. Blanes, F. Casas and A. Murua, On the numerical integration of ordinary differential equations by processed methods. SIAM J. Numer. Anal. 42 (2004) 531–552. [CrossRef] [MathSciNet]
  2. J.C. Butcher, The effective order of Runge-Kutta methods, in Proceedings of Conference on the Numerical Solution of Differential Equations, J.L. Morris Ed., Lect. Notes Math. 109 (1969) 133–139.
  3. P. Chartier, E. Faou and A. Murua, An algebraic approach to invariant preserving integrators: the case of quadratic and Hamiltonian invariants. Numer. Math. 103 (2006) 575–590. [CrossRef] [MathSciNet]
  4. D. Cottrell and P.F. Tupper, Energy drift in molecular dynamics simulations. BIT 47 (2007) 507–523. [CrossRef] [MathSciNet]
  5. E. Faou, E. Hairer and T.-L. Pham, Energy conservation with non-symplectic methods: examples and counter-examples. BIT 44 (2004) 699–709. [CrossRef] [MathSciNet]
  6. E. Hairer and C. Lubich, Symmetric multistep methods over long times. Numer. Math. 97 (2004) 699–723. [CrossRef] [MathSciNet]
  7. E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations, Springer Series in Computational Mathematics 31. Springer-Verlag, Berlin, 2nd Edition (2006).
  8. R.I. McLachlan and M. Perlmutter, Energy drift in reversible time integration. J. Phys. A 37 (2004) L593–L598. [CrossRef]
  9. I.P. Omelyan, Extrapolated gradientlike algorithms for molecular dynamics and celestial mechanics simulations. Phys. Rev. E 74 (2006) 036703. [CrossRef] [MathSciNet]
  10. G. Rowlands, A numerical algorithm for Hamiltonian systems. J. Comput. Phys. 97 (1991) 235–239. [CrossRef] [MathSciNet]
  11. 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. [CrossRef] [MathSciNet]
  12. R.D. Skeel, What makes molecular dynamics work? SIAM J. Sci. Comput. 31 (2009) 1363–1378. [CrossRef] [PubMed]
  13. D. Stoffer, On reversible and canonical integration methods. Technical Report SAM-Report No. 88-05, ETH-Zürich, Switzerland (1988).
  14. M. Takahashi and M. Imada, Monte Carlo calculation of quantum systems. II. Higher order correction. J. Phys. Soc. Jpn. 53 (1984) 3765–3769. [CrossRef]
  15. P.F. Tupper, Ergodicity and the numerical simulation of Hamiltonian systems. SIAM J. Appl. Dyn. Syst. 4 (2005) 563–587. [CrossRef] [MathSciNet]
  16. J. Wisdom, M. Holman and J. Touma, Symplectic correctors, in Integration Algorithms and Classical Mechanics, J.E. Marsden, G.W. Patrick and W.F. Shadwick Eds., Amer. Math. Soc., Providence R.I. (1996) 217–244.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you