Geodesic
Local one-dimensional scheme of the first initial-boundary value problem for the heat equation with a fractional derivative in the lower terms
News of the Kabardin-Balkar scientific center of RAS, no. 2 (2003), pp. 35-40

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In this work, a locally one-dimensional scheme is constructed for the heat equation with a fractional derivative in the lower terms. An a priori estimate in the uniform metric for solving the problem is obtained, which implies the convergence of the scheme in the uniform metric with speed $O(h+r)$.
Keywords: heat equation, locally one-dimensional scheme, fractional derivative, uniform metric 
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     author = {M. H. Shhanukov-Lafishev and F. M. Nakhusheva and M. H. Abregov},
     title = {Local one-dimensional scheme of the first initial-boundary value problem for the heat equation with a fractional derivative in the lower terms},
     journal = {News of the Kabardin-Balkar scientific center of RAS},
     pages = {35--40},
     publisher = {mathdoc},
     number = {2},
     year = {2003},
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     url = {http://geodesic.mathdoc.fr/item/IZKAB_2003_2_a4/}
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M. H. Shhanukov-Lafishev; F. M. Nakhusheva; M. H. Abregov. Local one-dimensional scheme of the first initial-boundary value problem for the heat equation with a fractional derivative in the lower terms. News of the Kabardin-Balkar scientific center of RAS, no. 2 (2003), pp. 35-40. http://geodesic.mathdoc.fr/item/IZKAB_2003_2_a4/