no. 4
Energy-preserving Runge-Kutta methods
ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 4, pp. 645-649.

We show that while Runge-Kutta methods cannot preserve polynomial invariants in general, they can preserve polynomials that are the energy invariant of canonical hamiltonian systems.

DOI : 10.1051/m2an/2009020
Classification : 65P10, 65L06
Mots clés : B-series, hamiltonian systems, energy-preserving integrators, Runge-Kutta methods 
@article{M2AN_2009__43_4_645_0,
     author = {Celledoni, Elena and McLachlan, Robert I. and McLaren, David I. and Owren, Brynjulf and G. Reinout W. Quispel and Wright, William M.},
     title = {Energy-preserving {Runge-Kutta} methods},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {645--649},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {4},
     year = {2009},
     doi = {10.1051/m2an/2009020},
     mrnumber = {2542869},
     zbl = {1169.65348},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2009020/}
}
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Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; G. Reinout W. Quispel; Wright, William M. Energy-preserving Runge-Kutta methods. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 4, pp. 645-649. doi : 10.1051/m2an/2009020. http://www.numdam.org/articles/10.1051/m2an/2009020/

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