The Validity of the Modified Equation for Nonlinear Shock Waves
Abstract
The modified (model, equivalent) equation is an important tool in designing and analyzing nonlinear difference schemes. In this note, the validity of this principle is rigorously established for nonlinear shock wave solutions and the upwind scheme in a particular case.
- Publication:
-
Journal of Computational Physics
- Pub Date:
- May 1985
- DOI:
- Bibcode:
- 1985JCoPh..58..336G
- Keywords:
-
- Difference Equations;
- Nonlinear Equations;
- Shock Waves;
- Taylor Series;
- Traveling Waves;
- Wave Equations;
- Discrete Functions;
- Finite Difference Theory;
- Series Expansion;
- Validity;
- Fluid Mechanics and Heat Transfer