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Zbl 1197.65082
Ramos, Higinio; Vigo-Aguiar, J.
On the frequency choice in trigonometrically fitted methods. (English)
[J] Appl. Math. Lett. 23, No. 11, 1378-1381 (2010). ISSN 0893-9659

Summary: The choice of frequency in trigonometrically fitted methods is a fundamental question, especially if long-term prediction is considered. For linear oscillators, the frequency of the method is the same as the frequency of the solution of the differential equation. However, for nonlinear problems the frequency of the method is, in general, different from the frequency of the true solution. We present some experiments showing how the frequency depends strongly on certain values.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general

Keywords: trigonometrically fitted methods; frequency determination; numerical examples; nonlinear second order initial value problems

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