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.
| Date of Award | Aug 17 2017 |
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| Original language | English (US) |
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| Awarding Institution | - Computer, Electrical and Mathematical Sciences and Engineering
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| Supervisor | David Ketcheson (Supervisor) |
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- Numerical analysis
- Splitting methods
- BDF-ADI
- absolute stability
- scour-cohn algorithm