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Scientific article
Open access
English

Achieving Brouwer's law with implicit Runge-Kutta methods

Published inBIT, vol. 48, no. 2, p. 231-243
Publication date2008
Abstract

In high accuracy long-time integration of differential equations, round-off errors may dominate truncation errors. This article studies the influence of round-off on the conservation of first integrals such as the total energy in Hamiltonian systems. For implicit Runge--Kutta methods, a standard implementation shows an unexpected propagation. We propose a modification that reduces the effect of round-off and shows a qualitative and quantitative improvement for an accurate integration over long times.

Keywords
  • Probabilistic error propagation
  • Implicit Runge--Kutta methods
  • Long-time integration
  • Efficient implementation
Citation (ISO format)
HAIRER, Ernst, MCLACHLAN, Robert I., RAZAKARIVONY, Alain. Achieving Brouwer’s law with implicit Runge-Kutta methods. In: BIT, 2008, vol. 48, n° 2, p. 231–243. doi: 10.1007/s10543-008-0170-3
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Article (Accepted version)
accessLevelPublic
Identifiers
ISSN of the journal0006-3835
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372downloads

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