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

MathSciNet review:
0084194

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References | Similar Articles | Additional Information

**[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 ∂²𝑢/∂𝑥²+∂²𝑢/∂𝑦²=∂𝑢/∂𝑡 by implicit methods*, J. Soc. Indust. Appl. Math.**3**(1955), 42–65. MR**0071875****[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**0080368****[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**0078754**, 10.1090/S0002-9939-1955-0078754-9**[5]**Stanley P. Frankel,*Convergence rates of iterative treatments of partial differential equations*, Math. Tables and Other Aids to Computation**4**(1950), 65–75. MR**0046149**, 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**0071874****[8]**David Young,*Iterative methods for solving partial difference equations of elliptic type*, Trans. Amer. Math. Soc.**76**(1954), 92–111. MR**0059635**, 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**

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DOI:
https://doi.org/10.1090/S0002-9947-1956-0084194-4

Article copyright:
© Copyright 1956
American Mathematical Society