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Energy-preserving Runge-Kutta methods

Published online by Cambridge University Press:  08 July 2009

Elena Celledoni ,
Robert I. McLachlan ,
David I. McLaren ,
Brynjulf Owren ,
G. Reinout W. Quispel  and
William M. Wright
Elena Celledoni
Affiliation:
Department of Mathematical Sciences, NTNU, 7491 Trondheim, Norway.
Robert I. McLachlan
Affiliation:
Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand. r.mclachlan@massey.ac.nz
David I. McLaren
Affiliation:
Mathematics Department, La Trobe University, VIC 3086, Australia.
Brynjulf Owren
Affiliation:
Department of Mathematical Sciences, NTNU, 7491 Trondheim, Norway.
G. Reinout W. Quispel
Affiliation:
Mathematics Department, La Trobe University, VIC 3086, Australia.
William M. Wright
Affiliation:
Mathematics Department, La Trobe University, VIC 3086, Australia.
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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.

Keywords

B-seriesHamiltonian systemsenergy-preserving integratorsRunge-Kutta methods.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 4: Special issue on Numerical ODEs today , July 2009 , pp. 645 - 649
Copyright
© EDP Sciences, SMAI, 2009

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