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Trigonometrically fitted explicit Numerov-type method for periodic ivps with two frequencies. (English) Zbl 1197.65085
Summary: New trigonometrically fitted Numerov type methods for the periodic initial problems are proposed. These methods are based on the original Numerov-type sixth order method with fifth internal stages motivated by {\it Ch. Tsitouras} [Comput. Math. Appl. 45, 37--42 (2003; Zbl 1035.65078)]. Some parameters are added to these methods so that they can integrate exactly the combination of trigonometrically functions with two frequencies. Numerical stability and phase properties of the new methods are analyzed. Numerical experiments are carried out to show the efficiency and robustness of our new methods in comparison with the well known codes proposed in the scientific literature.

65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
Full Text: DOI
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