Solution interpolation method for highly oscillating hyperbolic equations

This paper deals with a novel numerical scheme for hyperbolic equations with rapidly changing terms. we are especially interested in the quasilinear equation u t + a u x = f (x) u + g (x) u n and the wave equation u t t = f (x) u x x 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. © 2013 pilwon kim and chang hyeong lee.