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Controlling the error growth in long-term numerical integration of perturbed oscillations in one or several frequencies. (English) Zbl 1041.65058
Summary: 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.

65L05Initial value problems for ODE (numerical methods)
65L07Numerical investigation of stability of solutions of ODE
70-08Computational methods (mechanics of particles and systems)
34C15Nonlinear oscillations, coupled oscillators (ODE)
34E10Perturbations, asymptotics (ODE)
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