This paper deals with a novel numerical scheme for hyperbolic equations with rapidly changing terms. We are especially interested in the quasilinear equation and the wave equation that have a highly oscillating term like . 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.
Pilwon Kim. Chang Hyeong Lee. "Solution Interpolation Method for Highly Oscillating Hyperbolic Equations." J. Appl. Math. 2013 1 - 10, 2013. https://doi.org/10.1155/2013/546031