Exponentially fitted explicit Runge-Kutta-Nyström methods
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 \(\{ \exp(\lambda t)\), \(\exp (-\lambda t)\}\), \(\lambda\in\mathbb{C}\), or \(\{\sin(\omega t), \cos(\omega t)\}\) when \(\lambda=i\omega\), \(\omega\in\mathbb{R}\). 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.
scientific article; zbMATH DE number 2091367