Solution Interpolation Method for Highly Oscillating Hyperbolic Equations

Abstract EN

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.