Boundary-value problems for the heat conduction equation are considered in the case where the boundary conditions contain a fractional derivative. Problems of this type arise when the heat processes are simulated by a nonstationary heat flow by using the one-dimensional thermal model of a two-layer system (coating — base). It is proved that the problem under consideration is correct. A one-parameter family of difference schemes is constructed; it is shown that these schemes are stable and convergent in the uniform metric.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 9, pp. 1289–1398, September, 1993.
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Shkhanukov, M.K., Kerefov, A.A. & Berezovskii, A.A. Boundary-value problems for the heat conduction equation with a fractional derivative in the boundary conditions. Difference methods for numerical realization of these problems. Ukr Math J 45, 1445–1455 (1993). https://doi.org/10.1007/BF01058643
- Boundary Condition
- Heat Conduction
- Heat Flow
- Difference Scheme
- Difference Method