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2013 Solution Interpolation Method for Highly Oscillating Hyperbolic Equations
Pilwon Kim, Chang Hyeong Lee
J. Appl. Math. 2013: 1-10 (2013). DOI: 10.1155/2013/546031


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), ε1. 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.


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Pilwon Kim. Chang Hyeong Lee. "Solution Interpolation Method for Highly Oscillating Hyperbolic Equations." J. Appl. Math. 2013 1 - 10, 2013.


Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 06950741
MathSciNet: MR3138978
Digital Object Identifier: 10.1155/2013/546031

Rights: Copyright © 2013 Hindawi


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