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 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 eq...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/546031 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1110-757X 1687-0042 |