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Reducing round-off errors in symmetric multistep methods

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Paola Console and Ernst Hairer

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Abstract. Symmetric linear multistep methods have an excellent long-time behavior when applied to second order Hamiltonian systems with or without constraints. For high accuracy computations round-off can be the dominating source of errors. This article shows how symmetric multistep methods should be implemented, so that round-off errors are minimized and propagate like a random walk.

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Key Words. Symmetric linear multistep methods, constrained Hamiltonian systems, propagation of round-off error.

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