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Achieving Brouwer's law with implicit Runge-Kutta methods

Hairer, E. ; McLachlan, R. I. ; Razakarivony, A.

In: BIT Numerical Mathematics, 2008, vol. 48, no. 2, p. 231-243

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    Titre
    • Achieving Brouwer's law with implicit Runge-Kutta methods
    Auteur
    • Hairer, E.. Section de Mathématiques, Univ. de Genève, 1211, Genève 4, Switzerland
    • McLachlan, R. I.. Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand
    • Razakarivony, A.. Section de Mathématiques, Univ. de Genève, 1211, Genève 4, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • BIT Numerical Mathematics, 2008, vol. 48, no. 2, p. 231-243. Springer Netherlands
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:318518
    Summary
    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