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Zbl 1041.65058
Vigo-Aguiar, J.; Simos, T.E.; Ferrándiz, J.M.
Controlling the error growth in long-term numerical integration of perturbed oscillations in one or several frequencies. (English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 460, No. 2042, 561-567 (2004). ISSN 1364-5021; ISSN 1471-2946/e

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 2000:: *65L05 Initial value problems for ODE (numerical methods)
65L07 Numerical investigation of stability of solutions of ODE
70-08 Computational methods (mechanics of particles and systems)
34C15 Nonlinear oscillations of solutions of ODE
34E10 Asymptotic perturbations (ODE)

Keywords: numerical solution ODEs; periodic problems; exponential fitting methods

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Zentralblatt MATH Berlin [Germany]