A new family of Runge-Kutta type methods for the numerical integration of perturbed oscillators (Q1805867)

The subject of this article is the numerical treatment of initial value problems \(y''+\omega^2y=\varepsilon f(t,y,y')\), where \(\varepsilon\) is a small parameter and \(\omega\) a scalar quantity. Runge-Kutta-Nyström type methods, which integrate exactly the linear part of the problem, are introduced and fourth-order methods are constructed. Their global error behaves like \(O(\varepsilon \Delta t^4)\). Numerical experiments illustrate the efficieny of the new methods, when \(\varepsilon\) is small.