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Douglas, Jim jun.; Rachford, H. H. jun.

On the numerical solution of heat conduction problems in two and three space variables. (English) Zbl 0070.35401

Trans. Am. Math. Soc. 82, 421-439 (1956).
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Cited in 2 Reviews
Cited in 575 Documents

Keywords:

numerical analysis
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References:

[1] G. H. Bruce, D. W. Peaceman, H. H. Rachford, and J. D. Rice, Calculations of unsteady-state gas flow through porous media, Trans. Amer. Inst. Mining Metallurgical Engrs. vol. 198 (1953) pp. 79-91.
[2] Jim Douglas Jr., On the numerical integration of \partial ²\?/\partial \?²+\partial ²\?/\partial \?²=\partial \?/\partial \? by implicit methods, J. Soc. Indust. Appl. Math. 3 (1955), 42 – 65.
[3] 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. · Zbl 0072.14703
[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. · Zbl 0066.10502
[5] Stanley P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Tables and Other Aids to Computation 4 (1950), 65 – 75.
[6] William Edmund Milne, Numerical solution of differential equations, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. · Zbl 0050.12202
[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. · Zbl 0067.35801
[8] David Young, Iterative methods for solving partial difference equations of elliptic type, Trans. Amer. Math. Soc. 76 (1954), 92 – 111. · Zbl 0055.35704
[9] George G. O’Brien, Morton A. Hyman, and Sidney Kaplan, A study of the numerical solution of partial differential equations, J. Math. Physics 29 (1951), 223 – 251. · Zbl 0042.13204
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