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The Runge-Kutta-Wentzel-Kramers-Brillouin Method (1612.02288v2)
Published 3 Dec 2016 in physics.comp-ph and astro-ph.IM
Abstract: 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.