Solution Interpolation Method for Highly Oscillating Hyperbolic Equations

[摘要] This paper deals with a novel numerical scheme for hyperbolic equations withrapidly changing terms. We are especially interested in the quasilinear equationut+aux=f(x)u+g(x)unand the wave equationutt=f(x)uxxthat have a highlyoscillating term likef(x)=sin(x/ε),  ε≪1. It also applies to the equations involving rapidly changing or even discontinuous coefficients. The method is based on thesolution interpolation and the underlying idea is to establish a numerical scheme byinterpolating numerical data with a parameterized solution of the equation. While theconstructed numerical schemes retain the same stability condition, they carry bothquantitatively and qualitatively better performances than the standard method.

[学科分类] 应用数学