Geodesic
Energy-preserving Runge-Kutta methods
ESAIM: Mathematical Modelling and Numerical Analysis , Special issue on Numerical ODEs today, Tome 43 (2009) no. 4, pp. 645-649

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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
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 },
     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://geodesic.mathdoc.fr/articles/10.1051/m2an/2009020/}
}
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AU  - McLachlan, Robert I.
AU  - McLaren, David I.
AU  - Owren, Brynjulf
AU  - G. Reinout W. Quispel
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%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
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%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: Mathematical Modelling and Numerical Analysis , Special issue on Numerical ODEs today, Tome 43 (2009) no. 4, pp. 645-649. doi: 10.1051/m2an/2009020

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