Energy-preserving Runge-Kutta methods

Elena Celledoni; Robert I. McLachlan; David I. McLaren; Brynjulf Owren; G. Reinout W. Quispel; William M. Wright

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 4, page 645-649
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Celledoni, Elena, et al. "Energy-preserving Runge-Kutta methods." ESAIM: Mathematical Modelling and Numerical Analysis 43.4 (2009): 645-649. <http://eudml.org/doc/250591>.

@article{Celledoni2009,
abstract = { 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. },
author = {Celledoni, Elena, McLachlan, Robert I., McLaren, David I., Owren, Brynjulf, Reinout W. Quispel, G., Wright, William M.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {B-series; Hamiltonian systems; energy-preserving integrators; Runge-Kutta methods.; Runge-Kutta methods},
language = {eng},
month = {7},
number = {4},
pages = {645-649},
publisher = {EDP Sciences},
title = {Energy-preserving Runge-Kutta methods},
url = {http://eudml.org/doc/250591},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Celledoni, Elena
AU - McLachlan, Robert I.
AU - McLaren, David I.
AU - Owren, Brynjulf
AU - Reinout W. Quispel, G.
AU - Wright, William M.
TI - Energy-preserving Runge-Kutta methods
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2009/7//
PB - EDP Sciences
VL - 43
IS - 4
SP - 645
EP - 649
AB - 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.
LA - eng
KW - B-series; Hamiltonian systems; energy-preserving integrators; Runge-Kutta methods.; Runge-Kutta methods
UR - http://eudml.org/doc/250591
ER -

References

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