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

Author:
Jim Douglas

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

MSC:
Primary 65.3X

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

MathSciNet review:
0090876

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References | Similar Articles | Additional Information

**[1]**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****[2]**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****[3]**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**, https://doi.org/10.1090/S0002-9939-1955-0078754-9**[4]**J. Douglas, and D. W. Peaceman,*Numerical solution of two-dimensional heat flow problems*. A.I.Ch.E. Journal vol. 1 (1955) pp. 505-512.**[5]**William Edmund Milne,*Numerical solution of differential equations*, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. MR**0068321****[6]**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**

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

Article copyright:
© Copyright 1957
American Mathematical Society