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Some locally one-dimensional difference schemes for parabolic equations in an arbitrary region


Author: Bert Hubbard
Journal: Math. Comp. 20 (1966), 53-59
MSC: Primary 65.68
DOI: https://doi.org/10.1090/S0025-5718-1966-0187415-2
MathSciNet review: 0187415
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  • [1] J. H. Bramble and B. E. Hubbard, On the formulation of finite difference analogues of the Dirichlet problem for Poisson’s equation, Numer. Math. 4 (1962), 313–327. MR 0149672, https://doi.org/10.1007/BF01386325
  • [2] Jim Douglas Jr., On the numerical integration of ∂²𝑢/∂𝑥²+∂²𝑢/∂𝑦²=∂𝑢/∂𝑡 by implicit methods, J. Soc. Indust. Appl. Math. 3 (1955), 42–65. MR 0071875
  • [3] J. Douglas & J. Gunn, "A general formulation of alternating direction methods." (To appear.)
  • [4] Bert E. Hubbard, Alternating direction schemes for the heat equation in a general domain, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (1965), 448–463. MR 0196952
  • [5] D. W. Peaceman and H. H. Rachford Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl. Math. 3 (1955), 28–41. MR 0071874
  • [6] A. A. Samarskiĭ, An efficient difference method for solving a multidimensional parabolic equation in an arbitrary domain, Ž. Vyčisl. Mat. i Mat. Fiz. 2 (1962), 787–811 (Russian). MR 0183127

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DOI: https://doi.org/10.1090/S0025-5718-1966-0187415-2
Article copyright: © Copyright 1966 American Mathematical Society