Stability of BDF-ADI Discretizations

Abstract
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.

Citation
Felício Dos Reis, J. M. (2017). Stability of BDF-ADI Discretizations. KAUST Research Repository. https://doi.org/10.25781/KAUST-7HJ1T

DOI
10.25781/KAUST-7HJ1T

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