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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. Bramble & B. Hubbard, "On the formulation of finite difference analogues of the Dirichlet problem for Poisson's equation," Numer. Math., v. 4, 1962, pp. 313-327. MR 26 #7157. MR 0149672 (26:7157)
  • [2] J. Douglas, "On the numerical integration of $ {U_{xx}} + {U_{yy}} = {U_t}$ by implicit methods," J. Soc. Indust. Appl. Math., v. 3, 1955, pp. 42-65. MR 0071875 (17:196e)
  • [3] J. Douglas & J. Gunn, "A general formulation of alternating direction methods." (To appear.)
  • [4] B. Hubbard, "Alternating direction schemes for the heat equation in a general domain." (To appear.) MR 0196952 (33:5136)
  • [5] D. W. Peaceman, & H. H. Rachford, "The numerical solution of parabolic and elliptic differential equations," J. Soc. Indust. Appl. Math., v. 3, 1955, pp. 28-41. MR 17, 196. MR 0071874 (17:196d)
  • [6] A. A. Samarskii, "On an economical difference method for the solution of a multidimensional parabolic equation in an arbitrary region," Ž. Vyčisl. Mat. i Mat. Fiz., v. 2, 1962, pp. 787-811 (Russian); English transl., U.S.S.R. Comput. Math. and Math. Phys., v. 2, 1962, pp. 894-926. MR 0183127 (32:609)

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

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