Free Access
Issue
ESAIM: M2AN
Volume 43, Number 4, July-August 2009
Special issue on Numerical ODEs today
Page(s) 645 - 649
DOI https://doi.org/10.1051/m2an/2009020
Published online 08 July 2009
  1. M.-P. Calvo, A. Iserles and A. Zanna, Numerical solution of isospectral flows. Math. Comput. 66(1997) 1461–1486. [CrossRef]
  2. E. Celledoni, R.I. McLachlan, B. Owren and G.R.W. Quispel, Energy-preserving integrators and the structure of B-series. Preprint.
  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. G.J. Cooper, Stability of Runge-Kutta methods for trajectory problems. IMA J. Numer. Anal. 7 (1987) 1–13. [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, C. Lubich and G. Wanner, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations. Springer, Berlin, 2nd Edition (2006).
  7. A. Iserles and A. Zanna, Preserving algebraic invariants with Runge-Kutta methods. J. Comput. Appl. Math. 125 (2000) 69–81. [CrossRef] [MathSciNet]
  8. R.I. McLachlan, G.R.W. Quispel and G.S. Turner, Numerical integrators that preserve symmetries and reversing symmetries. SIAM J. Numer. Anal. 35 (1998) 586–599. [CrossRef] [MathSciNet]
  9. R.I. McLachlan, G.R.W. Quispel and N. Robidoux, Geometric integration using discrete gradients. Phil. Trans. Roy. Soc. A 357 (1999) 1021–1046. [CrossRef]
  10. G.R.W. Quispel and D.I. McLaren, A new class of energy-preserving numerical integration methods. J. Phys. A 41 (2008) 045206. [CrossRef] [MathSciNet]
  11. J.E. Scully, A search for improved numerical integration methods using rooted trees and splitting. MSc Thesis, La Trobe University, Australia (2002).
  12. L.F. Shampine, Conservation laws and the numerical solution of ODEs. Comput. Math. Appl. 12B (1986) 1287–1296. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]

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