A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators

A new embedded pair of explicit RKN methods specially adapted to the numerical integration of perturbed oscillators is obtained. This pair depends on a parameter v = ωh > 0 (h is the integration step and ω is the dominant frequency), and it has four stages and algebraic orders five and three. The numerical experiments carried out show that the new pair is very competitive when it is compared with high-quality codes proposed in the scientific literature.

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