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.
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://archive.numdam.org/articles/10.1051/m2an/2009020/}
}
TY - JOUR AU - Celledoni, Elena AU - McLachlan, Robert I. AU - McLaren, David I. AU - Owren, Brynjulf AU - G. Reinout W. Quispel AU - Wright, William M. TI - Energy-preserving Runge-Kutta methods JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 645 EP - 649 VL - 43 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2009020/ DO - 10.1051/m2an/2009020 LA - en ID - M2AN_2009__43_4_645_0 ER -
%0 Journal Article %A Celledoni, Elena %A McLachlan, Robert I. %A McLaren, David I. %A Owren, Brynjulf %A G. Reinout W. Quispel %A Wright, William M. %T Energy-preserving Runge-Kutta methods %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 645-649 %V 43 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2009020/ %R 10.1051/m2an/2009020 %G en %F 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: Modélisation mathématique et analyse numérique, Special issue on Numerical ODEs today, Tome 43 (2009) no. 4, pp. 645-649. doi : 10.1051/m2an/2009020. http://archive.numdam.org/articles/10.1051/m2an/2009020/
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