Solution Interpolation Method for Highly Oscillating Hyperbolic Equations

Pilwon Kim and Chang Hyeong Lee

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: This paper deals with a novel numerical scheme for hyperbolic equations with rapidly changing terms. We are especially interested in the quasilinear equation ut + aux = f(x)u + g(x)un and the wave equation utt = f(x)uxx that have a highly oscillating term like f(x) = sin(x/ε), ε ≪ 1. It also applies to the equations involving rapidly changing or even discontinuous coefficients. The method is based on the solution interpolation and the underlying idea is to establish a numerical scheme by interpolating numerical data with a parameterized solution of the equation. While the constructed numerical schemes retain the same stability condition, they carry both quantitatively and qualitatively better performances than the standard method.

Date: 2013
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https://doi.org/10.1155/2013/546031

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:546031

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