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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On stability criteria of explicit difference schemes for certain heat conduction problems with uncommon boundary conditions


Author: Arnold N. Lowan
Journal: Math. Comp. 15 (1961), 179-185
MSC: Primary 65.68
MathSciNet review: 0128632
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Abstract: Stability criteria are derived for the explicit difference schemes appropriate to the following problems: 1) heat conduction in a slab in contact with a well stirred liquid; 2) heat conduction in a slab radiating to one face of a thin slab with infinite thermal conductivity, the other face of which radiates into a medium at prescribed temperature; 3) heat conduction in a cylinder radiating to the inner surface of a thin coaxial cylindrical shell with infinite thermal conductivity, the outer surface of which radiates into a medium at prescribed temperature.


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

  • [1] A. N. Lowan, ``Heat conduction in a solid in contact with a well-stirred liquid,'' Phil. Mag., v. 17, 1934, p. 849-854.
  • [2] Walter P. Reid, Heat flow in a half space, Quart. Appl. Math. 14 (1956), 206–208. MR 0079488 (18,94c)
  • [3] Walter P. Reid, Heat flow in a cylinder, Quart. Appl. Math. 16 (1958), 147–153. MR 0093308 (19,1229j)
  • [4] A. N. Lowan, The Operator Approach to Problems of Stability and Convergence of Solutions of Difference Equations and the Convergence of Various Iteration Procedures, Scripta Mathematica, New York, 1957, p. 79.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1961-0128632-2
PII: S 0025-5718(1961)0128632-2
Article copyright: © Copyright 1961 American Mathematical Society