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), 421-439
MSC:
Primary 65.3X
DOI:
https://doi.org/10.1090/S0002-9947-1956-0084194-4
MathSciNet review:
0084194
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References | Similar Articles | Additional Information
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- [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 71875
- [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. MR 80368
- [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 78754, https://doi.org/10.1090/S0002-9939-1955-0078754-9
- [5] Stanley P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Tables Aids Comput. 4 (1950), 65–75. MR 46149, https://doi.org/10.1090/S0025-5718-1950-0046149-3
- [6] William Edmund Milne, Numerical solution of differential equations, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. MR 0068321
- [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 71874
- [8] David Young, Iterative methods for solving partial difference equations of elliptic type, Trans. Amer. Math. Soc. 76 (1954), 92–111. MR 59635, https://doi.org/10.1090/S0002-9947-1954-0059635-7
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1956-0084194-4
Article copyright:
© Copyright 1956
American Mathematical Society