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

  • A. A. Berezovsky
  • A. A. Kerefov
  • M. Kh. Shkhanukov-Lafishev

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.
Published
25.09.1993
How to Cite
BerezovskyA. A., KerefovA. A., and Shkhanukov-LafishevM. K. “Boundary-Value Problems for the Heat Conduction Equation With a Fractional Derivative in the Boundary Conditions. Difference Methods for Numerical Realization of These Problems”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 45, no. 9, Sept. 1993, pp. 1289–1398, https://umj.imath.kiev.ua/index.php/umj/article/view/5932.
Section
Research articles