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Zbl 1060.65073
Franco, J.M.
Exponentially fitted explicit Runge-Kutta-Nyström methods. (English)
[J] J. Comput. Appl. Math. 167, No. 1, 1-19 (2004). ISSN 0377-0427

The author derives so-called exponentially fitted Runge-Kutta-Nyström (EFRKN) schemes to numerically solve the Cauchy problem: $$y''=f(t,y),\quad t\in[t_0,T], \quad y(t_0)=y_0,\quad y'(t_0)=y_0'.$$ The EFRKN schemes integrate exactly differential systems whose solutions can be expressed as linear combination of the functions $\{ \exp(\lambda t)$, $\exp (-\lambda t)\}$, $\lambda\in\bbfC$, or $\{\sin(\omega t), \cos(\omega t)\}$ when $\lambda=i\omega$, $\omega\in\bbfR$. The author constructs explicit EFRKN methods with two and three stages and algebraic orders 3 an 4. He also discusses the problem of step length control and carries out numerical experiments.
[Erwin Schechter (Moers)]

MSC 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods
65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general

Keywords: oscillatory solutions; Cauchy problem; step length control; numerical experiments; exponential fitting; initial value problems; Runge-Kutta-Nyström methods

Cited in: Zbl 1136.65068

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