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