The Runge-Kutta-Wentzel-Kramers-Brillouin Method

We demonstrate the effectiveness of a novel scheme for numerically solving linear differential equations whose solutions exhibit extreme oscillation. We take a standard Runge-Kutta approach, but replace the Taylor expansion formula with a Wentzel-Kramers-Brillouin method. The method is demonstrated by application to the Airy equation, along with a more complicated burst-oscillation case. Finally, we compare our scheme to existing approaches.