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Boundary-value problems for the heat conduction equation with a fractional derivative in the boundary conditions. Difference methods for numerical realization of these problems

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Abstract

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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Authors and Affiliations

  1. Kabardino-Balkarskii University, USSR

    M. Kh. Shkhanukov & A. A. Kerefov

  2. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. A. Berezovskii

Authors
  1. M. Kh. Shkhanukov
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  2. A. A. Kerefov
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  3. A. A. Berezovskii
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Additional information

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

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  • DOI: https://doi.org/10.1007/BF01058643

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