Abstract
We propose an algorithm for calculating solutions of a difference Dirichlet problem for the Poisson equation on a seven-point nonorthogonal pattern of a rectangular grid. The algorithm is based on the incomplete reduction method. Bibliography: 4 titles.
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References
M. T. Bystrytskyi, “Convergence in a difference scheme for a nonorthogonal seven-point pattern of a rectangular grid,”Visnyk Kyivs'kogo Universytetu, No. 2, 149–160 (1997).
V. L. Makarov, S. V. Makarov, and M. N. Moskal'kov, “Spectral properties of difference Laplace operators on a hexagonal grid and some applications”Differential Equations,29, 1216–1221 (1993).
V. L. Makarov, S. V. Makarov, and M. M. Moskal'kov, “A fast algorithm for solving a difference Dirichlet problem on a hexagonal pattern for the Poisson equation on a rectangle,”Vychisl. Prikl. Mat.,77, 19–26 (1993).
A. A. Samarskii and E. S. Nikolaev,Methods of Solution of Equations on Grids [in Russian], Nauka, Moscow (1978).
Additional information
Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 15–22.
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Bystrytskyi, M.T. The incomplete reduction method for calculating solutions of a difference Dirichlet problem on a seven-point nonorthogonal pattern of a rectangular grid for the Poisson equation. J Math Sci 102, 3733–3739 (2000). https://doi.org/10.1007/BF02680225
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DOI: https://doi.org/10.1007/BF02680225