EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 49 / No 3 (May-June 2015) ESAIM: M2AN, 49 3 (2015) 695-711 References
Free Access
Issue
ESAIM: M2AN
Volume 49, Number 3, May-June 2015
Page(s) 695 - 711
DOI https://doi.org/10.1051/m2an/2014056
Published online 08 April 2015
  1. W. Bao, X. Dong and X. Zhao, Uniformly accurate multiscale time integrators for highly oscillatory second order differential equations. J. Math. Study 47 (2014) 111–150. [MathSciNet] [Google Scholar]
  2. G. Benettin, L. Galgani and A. Giorgilli, The dynamical foundations of classical statistical mechanics and the Boltzmann-Jeans conjecture. In Seminar on Dynamical Systems (St. Petersburg, 1991). Vol. 12 of Progr. Nonlin. Differ. Eq. Appl. Birkhäuser, Basel (1994) 3–14. [Google Scholar]
  3. F. Castella, P. Chartier and E. Faou, An averaging technique for highly oscillatory Hamiltonian problems. SIAM J. Numer. Anal. 47 (2009) 2808–2837. [CrossRef] [Google Scholar]
  4. P. Chartier, A. Murua and J.M. Sanz-Serna, Higher-order averaging, formal series and numerical integration I: B-series. Found. Comput. Math. 10 (2010) 695–727. [CrossRef] [MathSciNet] [Google Scholar]
  5. D. Cohen, Analysis and Numerical Treatment of Highly Oscillatory Differential Equations. Ph.D thesis, University of Geneva (2004). [Google Scholar]
  6. D. Cohen, E. Hairer and Ch. Lubich, Modulated Fourier expansions of highly oscillatory differential equations. Found. Comput. Math. 3 (2003) 327–345. [CrossRef] [MathSciNet] [Google Scholar]
  7. D. Cohen, E. Hairer and Ch. Lubich, Numerical energy conservation for multi-frequency oscillatory differential equations. BIT 45 (2005) 287–305. [Google Scholar]
  8. D. Cohen, T. Jahnke, K. Lorenz and Ch. Lubich, Numerical integrators for highly oscillatory Hamiltonian systems: a review. In Analysis, modeling and simulation of multiscale problems. Springer, Berlin (2006) 553–576. [Google Scholar]
  9. M. Condon, A. Deaño and A. Iserles, On second-order differential equations with highly oscillatory forcing terms. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 466 (2010) 1809–1828. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Condon, A. Deaño and A. Iserles, On systems of differential equations with extrinsic oscillation. Discrete Contin. Dyn. Syst. 28 (2010) 1345–1367. [CrossRef] [MathSciNet] [Google Scholar]
  11. M. Condon, A. Deaño and A. Iserles, Asymptotic solvers for oscillatory systems of differential equations. SFormula MA J. (2011) 79–101. [Google Scholar]
  12. E. Faou and K. Schratz, Asymptotic preserving schemes for the Klein–Gordon equation in the non-relativistic limit regime. Numerische Mathematik 126 (2013) 441–469. [Google Scholar]
  13. L. Gauckler, Long-time analysis of Hamiltonian partial differential equations and their discretizations. PhD. thesis, Universität Tübingen (2010). http://nbn-resolving.de/urn:nbn:de:bsz:21-opus-47540. [Google Scholar]
  14. V. Grimm and M. Hochbruck, Error analysis of exponential integrators for oscillatory second-order differential equations. J. Phys. A 39 (2006) 5495–5507. [CrossRef] [MathSciNet] [Google Scholar]
  15. E. Hairer and Ch. Lubich, Long-time energy conservation of numerical methods for oscillatory differential equations. SIAM J. Numer. Anal. 38 (electronic) (2000) 414–441. [CrossRef] [Google Scholar]
  16. E. Hairer, Ch. Lubich and G. Wanner, Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations. Vol. 31 of Springer Ser. Comput. Math. Springer, Berlin (2002). [Google Scholar]
  17. M. Hochbruck and Ch. Lubich, A Gautschi-type method for oscillatory second-order differential equations. Numer. Math. 83 (1999) 403–426. [CrossRef] [MathSciNet] [Google Scholar]
  18. M. Hochbruck and A. Ostermann, Exponential integrators. Acta Numerica 19 (2010) 209–286. [Google Scholar]
  19. C. Le Bris and F. Legoll, Integrators for highly oscillatory Hamiltonian systems: an homogenization approach. Discrete Contin. Dyn. Syst. Ser. B 13 (2010) 347–373. [MathSciNet] [Google Scholar]
  20. R.I. McLachlan and A. Stern, Modified trigonometric integrators. SIAM J. Numer. Anal. 52 (2014) 1378–1397. [CrossRef] [Google Scholar]
  21. A. Stern and E. Grinspun, Implicit-explicit variational integration of highly oscillatory problems. Multiscale Model. Simul. 7 (2009) 1779–1794. [CrossRef] [Google Scholar]
  22. M. Tao, H. Owhadi and J.E. Marsden, Nonintrusive and structure preserving multiscale integration of stiff ODEs, SDEs, and Hamiltonian systems with hidden slow dynamics via flow averaging. Multiscale Model. Simul. 8 (2010) 1269–1324. [CrossRef] [Google Scholar]
  23. B. Wang and X. Wu, A new high precision energy-preserving integrator for system of oscillatory second-order differential equations. Phys. Lett. A 376 (2012) 1185–1190. [CrossRef] [Google Scholar]

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