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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
• [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. MR 0040805

Bibliography

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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.

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J. Douglas, On the numerical integration of by implicit methods, J. Soc. Ind. Appl. Math. vol. 3 (1955) pp. 42-65. MR 0071875 (17:196e)

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-, 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)

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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. 787-793. MR 0078754 (17:1241i)

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S. P. Frankel, Convergence rates of iterative treatments of partial differential equations, Math. Tables and Other Aids to Computation vol. 4 (1950) pp. 65-75. MR 0046149 (13:692e)

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W. E. Milne. Numerical solution of differential equations, New York, 1953. MR 0068321 (16:864c)

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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. 28-41. MR 0071874 (17:196d)

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D. Young, Iterative methods for solving partial difference equations of elliptic type, Trans. Amer. Math. Soc. vol. 76 (1954) pp. 92-111. MR 0059635 (15:562b)

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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. 223-251. MR 0040805 (12:751e)