Energy-preserving Runge-Kutta methods
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 4, p. 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 : https://doi.org/10.1051/m2an/2009020
Classification:  65P10,  65L06
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {4},
     year = {2009},
     pages = {645-649},
     doi = {10.1051/m2an/2009020},
     zbl = {1169.65348},
     mrnumber = {2542869},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2009__43_4_645_0}
}
Celledoni, Elena; McLachlan, Robert I.; McLaren, David I.; Owren, Brynjulf; G. Reinout W. Quispel; Wright, William M. Energy-preserving Runge-Kutta methods. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 4, pp. 645-649. doi : 10.1051/m2an/2009020. http://www.numdam.org/item/M2AN_2009__43_4_645_0/

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