Some locally onedimensional difference schemes for parabolic equations in an arbitrary region
Author:
Bert Hubbard
Journal:
Math. Comp. 20 (1966), 5359
MSC:
Primary 65.68
MathSciNet review:
0187415
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References 
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Additional Information
 [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
(26 #7157)
 [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
(17,196e)
 [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
(33 #5136)
 [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
(17,196d)
 [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 (32 #609)
 [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. 313327. MR 26 #7157. MR 0149672 (26:7157)
 [2]
 J. Douglas, "On the numerical integration of by implicit methods," J. Soc. Indust. Appl. Math., v. 3, 1955, pp. 4265. 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. 2841. 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. 787811 (Russian); English transl., U.S.S.R. Comput. Math. and Math. Phys., v. 2, 1962, pp. 894926. MR 0183127 (32:609)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196601874152
PII:
S 00255718(1966)01874152
Article copyright:
© Copyright 1966
American Mathematical Society
