Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [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 $ {u_{xx}} + {u_{yy}} = {u_t}$ 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)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 65.3X

Retrieve articles in all journals with MSC: 65.3X

Additional Information

Article copyright: © Copyright 1956 American Mathematical Society

American Mathematical Society