Free Access
Issue
ESAIM: M2AN
Volume 43, Number 4, July-August 2009
Special issue on Numerical ODEs today
Page(s) 651 - 676
DOI https://doi.org/10.1051/m2an/2009028
Published online 08 July 2009
  1. D. Bambusi and B. Grebert, Birkhoff normal form for PDEs with tame modulus. Duke Math. J. 135 (2006) 507–567. [CrossRef] [MathSciNet]
  2. C. Besse, B. Bidégaray and S. Descombes, Order estimates in time of splitting methods for the nonlinear Schrödinger equation. SIAM J. Numer. Anal. 40 (2002) 26–40. [CrossRef] [MathSciNet]
  3. B. Cano, Conserved quantities of some Hamiltonian wave equations after full discretization. Numer. Math. 103 (2006) 197–223. [CrossRef] [MathSciNet]
  4. D. Cohen, E. Hairer and C. Lubich, Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions. Arch. Ration. Mech. Anal. 187 (2008) 341–368. [CrossRef] [MathSciNet]
  5. G. Dujardin, Analyse de méthodes d'intégration en temps des équation de Schrödinger. Ph.D. Thesis, University Rennes 1, France (2008).
  6. G. Dujardin and E. Faou, Normal form and long time analysis of splitting schemes for the linear Schrödinger equation with small potential. Numer. Math. 108 (2007) 223–262. [CrossRef] [MathSciNet]
  7. G. Dujardin and E. Faou, Long time behavior of splitting methods applied to the linear Schrödinger equation. C. R. Math. Acad. Sci. Paris 344 (2007) 89–92. [CrossRef] [MathSciNet]
  8. H.L. Eliasson and S.B. Kuksin, KAM for non-linear Schrödinger equation. Preprint (2006).
  9. E. Hairer, S.P. Nørsett and G. Wanner, Solving Ordinary Differential Equations I. Nonstiff Problems, Springer Series in Computational Mathematics 8. Second Edition, Springer, Berlin (1993).
  10. E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration – Structure-preserving Algorithms for Ordinary Differential Equations. Springer, Berlin (2002).
  11. T. Jahnke and C. Lubich, Error bounds for exponential operator splittings. BIT 40 (2000) 735–744. [CrossRef] [MathSciNet]
  12. B. Leimkuhler and S. Reich, Simulating Hamiltonian dynamics, Cambridge Monographs on Applied and Computational Mathematics 14. Cambridge University Press, Cambridge (2004).
  13. C. Lubich, On splitting methods for the Schödinger-Poisson and cubic nonlinear Schrödinger equations. Math. Comp. 77 (2008) 2141–2153. [CrossRef] [MathSciNet]
  14. M. Oliver, M. West and C. Wulff, Approximate momentum conservation for spatial semidiscretizations of semilinear wave equations. Numer. Math. 97 (2004) 493–535. [CrossRef] [MathSciNet]
  15. Z. Shang, Resonant and Diophantine step sizes in computing invariant tori of Hamiltonian systems. Nonlinearity 13 (2000) 299–308. [CrossRef] [MathSciNet]

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