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Zbl 0991.65062
Vanden Berghe, G.; Ixaru, L.Gr.; De Meyer, H.
Frequency determination and step-length control for exponentially-fitted Runge-Kutta methods.
(English)
[J] J. Comput. Appl. Math. 132, No.1, 95-105 (2001). ISSN 0377-0427

Summary: An exponentially fitted Runge-Kutta (EFRK) fifth-order method with six stages is constructed, which exactly integrates first-order differential initial-value problems whose solutions are linear combinations of functions of the form $\{\exp(\omega x),\exp(-\omega x)\}$, ($\omega\in\bbfR$ or $i\bbfR$). By combining this EFRK method with an equivalent classical embedded (4,5) Runge-Kutta method, a technique is developed for the estimation of the occurring $\omega$-values. Error and step-length control is carried out by using the Richardson extrapolation procedure. Some numerical experiments show the efficiency of the introduced methods.
MSC 2000:
*65L06 Multistep, Runge-Kutta, and extrapolation methods
65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
65L50 Mesh generation and refinement (ODE)
65L70 Error bounds (numerical methods for ODE)

Keywords: error control; explicit Runge-Kutta methods; initial-value problems; oscillating solutions; exponential fitting; step-length control; Richardson extrapolation; numerical experiments

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