Achieving Brouwer’s law with implicit Runge–Kutta methods
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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.
Key wordsround-off error probabilistic error propagation implicit Runge–Kutta methods long-time integration efficient implementation
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