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On the frequency choice in trigonometrically fitted methods. (English) Zbl 1197.65082

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:

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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References:

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