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Zbl 1225.65072
Fang, Yonglei; Song, Yongzhong; Wu, Xinyuan
New embedded pairs of explicit Runge-Kutta methods with FSAL properties adapted to the numerical integration of oscillatory problems. (English)
[J] Phys. Lett., A 372, No. 44, 6551-6559 (2008). ISSN 0375-9601

Summary: A higher order Runge-Kutta (pair) method specially adapted to the numerical integration of IVPs with oscillatory solutions is presented. This method is based on the adapted methods proposed by {\it J.M. Franco} [Appl. Numer. Math. 50, No. 3-4, 427--443 (2004; Zbl 1057.65043)]). We give explicit method (up to order 5) as well as pairs of embedded Runge-Kutta methods of order 5 and 4 designed using the FSAL properties. The stability of the new methods is analyzed. The numerical experiments are carried out to show the efficiency and robustness of our methods in comparison with some efficient methods.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
65L06 Multistep, Runge-Kutta, and extrapolation methods

Keywords: embedded pairs; adapted RK methods; oscillatory problems; FSAL technique; absolute stability

Citations: Zbl 1057.65043

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