Abstract
We propose a new high-order finite difference discretization strategy, which is based on the Richardson extrapolation technique and an operator interpolation scheme, to solve convection diffusion equations. For a particular implementation, we solve a fine grid equation and a coarse grid equation by using a fourth-order compact difference scheme. Then we combine the two approximate solutions and use the Richardson extrapolation to compute a sixth-order accuracy coarse grid solution. A sixth-order accuracy fine grid solution is obtained by interpolating the sixth-order coarse grid solution using an operator interpolation scheme. Numerical results are presented to demonstrate the accuracy and efficacy of the proposed finite difference discretization strategy, compared to the sixth-order combined compact difference (CCD) scheme, and the standard fourth-order compact difference (FOC) scheme.
| Original language | English |
|---|---|
| Pages (from-to) | 18-32 |
| Number of pages | 15 |
| Journal | Numerical Methods for Partial Differential Equations |
| Volume | 20 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2004 |
Keywords
- CCD scheme
- Compact difference scheme
- Convection diffusion equation
- Richardson extrapolation
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics