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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.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L07 Numerical investigation of stability of solutions to ordinary differential equations
70-08 Computational methods for problems pertaining to mechanics of particles and systems
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34E10 Perturbations, asymptotics of solutions to ordinary differential equations
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