Convergence Analysis of the ADI Scheme for Parabolic Problems using Discrete Harmonic Functions

Computational Mathematics and Mathematical Physics（2022）

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摘要

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 √(ln(1/h)) factor, the second order bound that is stated without a proof by Samarski [8].

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关键词

heat equation, finite difference, ADI, convergence analysis

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