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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[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****[3]**Walter P. Reid,*Heat flow in a cylinder*, Quart. Appl. Math.**16**(1958), 147–153. MR**0093308****[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.

Retrieve articles in *Mathematics of Computation*
with MSC:
65.68

Retrieve articles in all journals with MSC: 65.68

Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1961-0128632-2

Article copyright:
© Copyright 1961
American Mathematical Society