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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**[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]**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)****[3]**-,*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)****[4]**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)****[5]**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)****[6]**W. E. Milne.*Numerical solution of differential equations*, New York, 1953. MR**0068321 (16:864c)****[7]**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)****[8]**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)****[9]**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)**

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

Article copyright:
© Copyright 1956
American Mathematical Society