The locally-one-dimensional scheme for the equation of heat conductivity with the concentrated thermal capacity

Shkhanukov-Lafishev, M. H. , Lafisheva M. M. , Nakhusheva F. M. , Mambetova A. B.
Vladikavkaz Mathematical Journal 2013. Vol. 15. Issue 4.

Abstract:
The work is devoted to locally-one-dimensional schemes for the equation of heat conductivity with a non-stationary boundary condition which imitate a concentrated thermal capacity placed on domain boundary. A priori estimate in the uniform metrics is obtained and the convergence of the constructed scheme on a cubic net is proved.

Keywords: the regional problem, the concentrated thermal capacity, the locally-one-dimensional schemes, convergence, an aprioristic estamation

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