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Achieving Brouwer's law with implicit Runge-Kutta methods

McLachlan, Robert I.
Razakarivony, Alain
Published in BIT Numerical Mathematics. 2008, vol. 48, no. 2, p. 231-243
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 propagationImplicit Runge--Kutta methodsLong-time integrationEfficient implementation.
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HAIRER, Ernst, MCLACHLAN, Robert I., RAZAKARIVONY, Alain. Achieving Brouwer's law with implicit Runge-Kutta methods. In: BIT Numerical Mathematics, 2008, vol. 48, n° 2, p. 231-243. https://archive-ouverte.unige.ch/unige:5205

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Deposited on : 2010-02-16

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