@article{f7be070bd97f46a19477a29df4cea73c,

title = "Convergence Analysis of the ADI Scheme for Parabolic Problems using Discrete Harmonic Functions",

abstract = "Abstract: For the heat equation on a rectangle, we consider the finite difference ADI method without a perturbation term on vertical sides for the intermediate solution. Using stability results of Andreev [1, 2] for the discrete harmonic function we prove, except for a $$\sqrt {\ln(1{\text{/}}h)} $$ factor, the second order bound that is stated without a proof by Samarski [8].",

keywords = "ADI, convergence analysis, finite difference, heat equation",

author = "B. Bialecki and M. Dryja and R. Fernandes",

note = "Funding Information: This research was supported in part by the Technion Vice President for Research Fund—New York Metropolitan Research Fund and in part by Israeli Ministry of Science Grant No. 01-01-01509. This work has also been supported in part by the IST Programmes of the EU as Shared-cost RTD (FET Open) Projects under Contract No. IST-2000-26473 (ECG—Effective Computational Geometry for Curves and Surfaces) and No. IST-2001-39250 (MOVIE—Motion Planning in Virtual Environments), by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (Center for Geometric Computing and its Applications), and by the Hermann Minkowski—Minerva Center for Geometry at Tel Aviv University. Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",

year = "2022",

month = feb,

doi = "10.1134/S096554252202004X",

language = "British English",

volume = "62",

pages = "183--197",

journal = "Computational Mathematics and Mathematical Physics",

issn = "0965-5425",

publisher = "Pleiades Publishing",

number = "2",

}