Geodesic
Stability and convergence of the locally one-dimensional scheme A.~A.~Samarskii,
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 27 (2023) no. 3, pp. 407-426

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The first initial-boundary value problem for a multidimensional (in space variables) integro-differential equation of convection-diffusion is studied. For an approximate solution of the problem a locally one-dimensional scheme by A. A. Samarskii with order of approximation $O(h^2+\tau)$ is proposed. The study of the uniqueness and stability of the solution is carried out using the method of energy inequalities. A priori estimates for the solution of a locally one-dimensional difference scheme are obtained, which imply the uniqueness of the solution, the continuous and uniform dependence of the solution on the input data, and the convergence of the solution of the scheme to the solution of the original differential problem at a rate equal to the order of approximation of the difference scheme. For a two-dimensional problem, a numerical solution algorithm is constructed, numerical calculations of test cases are carried out, illustrating the theoretical results obtained in the study.
Mots-clés : convection-diffusion equation, nonlocal source
Keywords: first initial boundary value problem, multidimensional problem, difference schemes, a priori estimate, stability and convergence. 
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     author = {Z. V. Beshtokova},
     title = {Stability and convergence of the locally one-dimensional scheme {A.~A.~Samarskii,}},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {407--426},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2023_27_3_a0/}
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Z. V. Beshtokova. Stability and convergence of the locally one-dimensional scheme A.~A.~Samarskii,. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 27 (2023) no. 3, pp. 407-426. http://geodesic.mathdoc.fr/item/VSGTU_2023_27_3_a0/