Controlling the error growth in long–term numerical integration of perturbed oscillations in one or several frequencies

In this paper we present a simple technique that allows us to limit the error growth in the long–term numerical integration of perturbed multi–dimensional oscillators, while using highly efficient and accurate special multi–step codes. After laying down the theoretical basis of their behaviour, we then illustrate them with some numerical examples, including a case with non–resonant frequencies, seldom found in the related literature.

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