A note on the alternating direction implicit method for the numerical solution of heat flow problems

A note on the alternating direction implicit method for the numerical solution of heat flow problems
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by Jim Douglas

Proc. Amer. Math. Soc. 8 (1957), 409-412

DOI: https://doi.org/10.1090/S0002-9939-1957-0090876-7

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References

Jim Douglas Jr., On the numerical integration of $\partial ^2u/\partial x^2+\partial ^2u/\partial y^2=\partial u/\partial t$ by implicit methods, J. Soc. Indust. Appl. Math. 3 (1955), 42–65. MR 71875
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
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, DOI 10.1090/S0002-9939-1955-0078754-9

Numerical solution of two-dimensional heat flow problems

William Edmund Milne, Numerical solution of differential equations, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0068321
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