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English

Achieving Brouwer's law with implicit Runge-Kutta methods

Contributors

Hairer, Ernst; McLachlan, Robert I.; Razakarivony, Alain

Published in

BIT, vol. 48, no. 2, p. 231-243

Publication date

2008

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

UNIGE affiliation entities

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

Main files (1)

Article (Accepted version)

Identifiers

Additional URL for this publication

http://www.springerlink.com/content/a03722g024535g42/?p=508868c1faa842cdb97813e07d3cea30&pi=0

Journal ISSN

0006-3835
674views
572downloads

Technical informations

Creation

16/02/2010 11:50:00

First validation

16/02/2010 11:50:00

Update

14/03/2023 15:24:06

Status update

14/03/2023 15:24:06

Last indexation

29/10/2024 13:00:41
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