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arXiv · 1612.02288

The Runge-Kutta-Wentzel-Kramers-Brillouin Method

W. J. Handley·A. N. Lasenby·M. P. Hobson
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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.

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W. J. Handley, A. N. Lasenby, M. P. Hobson. 2016-12-09. The Runge-Kutta-Wentzel-Kramers-Brillouin Method. https://arxiv.org/abs/1612.02288

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