Abstract
We present an analysis of an Alternating Direction Implicit (ADI) scheme for a linear, singularly perturbed reaction-diffusion equation. By providing an expression for the error that separates the temporal and spatial components, we can use existing results for steady-state problems to give a succinct analysis for the time-dependent problem, and that generalizes for various layer-adapted meshes. We report the results of numerical experiments that support the theoretical findings. In addition, we provide a numerical comparison between the ADI and Euler techniques, as well details of the computational advantage gained by parallelizing the algorithm.
| Original language | English |
|---|---|
| Pages (from-to) | 507-519 |
| Number of pages | 13 |
| Journal | International Journal of Numerical Analysis and Modeling |
| Volume | 7 |
| Issue number | 3 |
| Publication status | Published - 2010 |
Keywords
- Alternating directions
- Layer-adapted meshes
- Reaction-diffusion problems
- Singular perturbation