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Zbl 0948.65066
Vanden Berghe, G.; De Meyer, H.; Van Daele, M.; Van Hecke, T.
Exponentially-fitted explicit Runge-Kutta methods. (English)
[J] Comput. Phys. Commun. 123, No.1-3, 7-15 (1999). ISSN 0010-4655

It is pointed out that explicit Runge-Kutta methods cannot integrate polynomial solutions of degree greater than 1 exactly, except in the case of quadrature problems. Considerations based on this observation lead to the design of a new exponentially-fitted method. The new method is compared with the method of {\it T. E. Simos} [Appl. Math. Lett. 9, No. 6, 61-66 (1996; Zbl 0864.65052)] and, as for the Simos method, is superior in performance over a classical method for some oscillatory problems. For two further test problems, almost perfect accuracy is achieved by the new method. However, this is evidently because the method integrates problems with purely oscillatory solutions exactly.
[J.C.Butcher (Auckland)]

MSC 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods
65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: explicit Runge-Kutta methods; initial-value problems; oscillating solutions; exponential fitting; performance; numerical examples

Citations: Zbl 0864.65052

Cited in: Zbl 1039.65055

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