Free access
Issue
ESAIM: M2AN
Volume 43, Number 4, July-August 2009
Special issue on Numerical ODEs today
Page(s) 607 - 630
DOI http://dx.doi.org/10.1051/m2an/2009029
Published online 08 July 2009
  1. H. Berland and B. Owren, Algebraic structures on ordered rooted trees and their significance to Lie group integrators, in Group theory and numerical analysis, CRM Proc. Lecture Notes, Amer. Math. Soc., Providence R.I. (2005) 49–63.
  2. N. Bourbaki, Lie groups and Lie algebras. Springer-Verlag, Berlin-New York (1989).
  3. J.C. Butcher, An algebraic theory of integration methods. Math. Comput. 26 (1972) 79–106. [CrossRef]
  4. P. Cartier, A primer of Hopf algebras, in Frontiers in number theory, physics, and geometry II. Springer, Berlin (2007) 537–615.
  5. P. Chartier and A. Murua, Preserving first integrals and volume forms of additively split systems. IMA J. Numer. Anal. 27 (2007) 381–405. [CrossRef] [MathSciNet]
  6. P. Chartier, E. Faou and A. Murua, An algebraic approach to invariant preserving integators: the case of quadratic and Hamiltonian invariants. Numer. Math. 103 (2006) 575–590. [CrossRef] [MathSciNet]
  7. A. Connes and H. Moscovici, Hopf algebras, cyclic cohomology and the transverse index theorem. Commun. Math. Phys. 198 (1998).
  8. A. Dür, Möbius functions, incidence algebras and power-series representations, in Lecture Notes in Mathematics 1202, Springer-Verlag (1986).
  9. E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration – Structure-Preserving Algorithms for Ordinary Differential Equations, Second edition, Springer Series in Computational Mathematics 31. Springer, Berlin (2006).
  10. G.P. Hochschild, Basic theory of algebraic groups and Lie algebras. Springer-Verlag (1981).
  11. M.E. Hoffman, Quasi-shuffle products. J. Algebraic Comb. 11 (2000) 49–68. [CrossRef]
  12. D. Kreimer, On the Hopf algebra structure of perturbative quantum field theories. Adv. Theor. Math. Phys. 2 (1998) 303–334. [MathSciNet]
  13. J. Milnor and J. Moore, On the structure of Hopf algebras. Ann. Math. 81 (1965) 211–264. [CrossRef]
  14. H. Munthe-Kaas and W. Wright, On the Hopf algebraic structure of Lie group integrators. Found. Comput. Math. 8 (2008) 227–257. [CrossRef] [MathSciNet]
  15. A. Murua, Formal series and numerical integrators, Part i: Systems of ODEs and symplectic integrators. Appl. Numer. Math. 29 (1999) 221–251. [CrossRef] [MathSciNet]
  16. A. Murua, The Hopf algebra of rooted trees, free Lie algebras, and Lie series. Found. Comput. Math. 6 (2006) 387–426. [CrossRef] [MathSciNet]
  17. A. Murua and J.M. Sanz-Serna, Order conditions for numerical integrators obtained by composing simpler integrators. Phil. Trans. R. Soc. A 357 (1999) 1079–1100. [CrossRef]

Recommended for you