On the numerical solution of heat conduction problems in two and three space variables
Authors:
Jim Douglas and H. H. Rachford
Journal:
Trans. Amer. Math. Soc. 82 (1956), 421439
MSC:
Primary 65.3X
MathSciNet review:
0084194
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References 
Similar Articles 
Additional Information
 [1]
G. H. Bruce, D. W. Peaceman, H. H. Rachford, and J. D. Rice, Calculations of unsteadystate gas flow through porous media, Trans. Amer. Inst. Mining Metallurgical Engrs. vol. 198 (1953) pp. 7991.
 [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)
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Jim
Douglas Jr., On the relation between stability and convergence in
the numerical solution of linear parabolic and hyperbolic differential
equations, J. Soc. Indust. Appl. Math. 4 (1956),
20–37. MR
0080368 (18,236d)
 [4]
Jim
Douglas Jr. and T.
M. Gallie Jr., Variable time steps in the solution of
the heat flow equation by a difference equation, Proc. Amer. Math. Soc. 6 (1955), 787–793. MR 0078754
(17,1241i), http://dx.doi.org/10.1090/S00029939195500787549
 [5]
Stanley
P. Frankel, Convergence rates of iterative
treatments of partial differential equations, Math. Tables and Other Aids to Computation 4 (1950), 65–75. MR 0046149
(13,692e), http://dx.doi.org/10.1090/S00255718195000461493
 [6]
William
Edmund Milne, Numerical solution of differential equations,
John Wiley & Sons Inc., New York, 1953. MR 0068321
(16,864c)
 [7]
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)
 [8]
David
Young, Iterative methods for solving partial
difference equations of elliptic type, Trans.
Amer. Math. Soc. 76
(1954), 92–111. MR 0059635
(15,562b), http://dx.doi.org/10.1090/S00029947195400596357
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George
G. O’Brien, Morton
A. Hyman, and Sidney
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equations, J. Math. Physics 29 (1951), 223–251.
MR
0040805 (12,751e)
 [1]
 G. H. Bruce, D. W. Peaceman, H. H. Rachford, and J. D. Rice, Calculations of unsteadystate gas flow through porous media, Trans. Amer. Inst. Mining Metallurgical Engrs. vol. 198 (1953) pp. 7991.
 [2]
 J. Douglas, On the numerical integration of by implicit methods, J. Soc. Ind. Appl. Math. vol. 3 (1955) pp. 4265. MR 0071875 (17:196e)
 [3]
 , On the relation between stability and convergence in the numerical solution of linear parabolic and hyperbolic differential equations, to appear in J. Soc. Ind. Appl. Math. vol. 4. MR 0080368 (18:236d)
 [4]
 J. Douglas and T. M. Gallie, Variable time steps in the solution of the heat flow equation by a difference equation, Proc. Amer. Math. Soc. vol. 6 (1955) pp. 787793. MR 0078754 (17:1241i)
 [5]
 S. P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Tables and Other Aids to Computation vol. 4 (1950) pp. 6575. MR 0046149 (13:692e)
 [6]
 W. E. Milne. Numerical solution of differential equations, New York, 1953. MR 0068321 (16:864c)
 [7]
 D. W. Peaceman and H. H. Rachford, The numerical solution of parabolic and elliptic differential equations, J. Soc. Ind. Appl. Math. vol. 3 (1953) pp. 2841. MR 0071874 (17:196d)
 [8]
 D. Young, Iterative methods for solving partial difference equations of elliptic type, Trans. Amer. Math. Soc. vol. 76 (1954) pp. 92111. MR 0059635 (15:562b)
 [9]
 G. G. O'Brien, M. A. Hyman and S. Kaplan, A study of the numerical solution of partial differential equations, Journal of Mathematics and Physics vol. 29 (1951) pp. 223251. MR 0040805 (12:751e)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947195600841944
PII:
S 00029947(1956)00841944
Article copyright:
© Copyright 1956 American Mathematical Society
