We present new results on absolute stability for BDF-ADI (Backward differentiation formula Alternating Direction Implicit) methods applied to a linear advection and diffusion equations. Unconditional absolute stability of the BDF2-ADI method is proven for advection and diffusion separately, as well as to the BDF3-ADI method for the purely-diffusive case. Conditional absolute stability of the BDF4-ADI is also proven for the purely-diffusive case, and stability regions for BDF3-ADI and BDF4- ADI are given in terms of the PDE coefficients and numerical parameters. Lastly, numerical experiments are presented to support the theoretical results and conjectures. These experiments also suggest future work.
| Identifer | oai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/625356 |
| Date | 17 August 2017 |
| Creators | Felício dos Reis, João Miguel |
| Contributors | Ketcheson, David I., Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, Keyes, David E., Michels, Dominik L., Loczi, Lajos |
| Source Sets | King Abdullah University of Science and Technology |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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