Abstract
It is generally agreed that the alternating-direction implicit iterative methods for the solution of the finite-difference approximations to partial differential equations, in particular those of elliptic type, are the best, even with a geometric distribution of the parameters. It can be established rigorously in the case of the “model problem”, that the approximate attenuations per cycle of the component of the dominant eigenvector are as follows
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Todd, J. (1967). Optimal ADI - Parameters. In: Collatz, L., Meinardus, G., Unger, H. (eds) Funktionalanalysis Approximationstheorie Numerische Mathematik. Internationale Schriftenreihe zur Numerischen Mathematik / International Series of Numerical Mathematics / Série Internationale D’Analyse Numérique, vol 7. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5821-2_8
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DOI: https://doi.org/10.1007/978-3-0348-5821-2_8
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5822-9
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