Geodesic
On strong solutions of a $B$-elliptic boundary-value problem and its difference approximation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 2, Tome 236 (2024), pp. 3-12

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In this work, a finite-difference scheme for a boundary-value problem for a $B$-elliptic equation is constructed. The convergence is examined in the Kipriyanov weight space. An integral balance relation for the exact solution of the original problem is obtained by using Steklov averaging operators. A five-point difference scheme and an a priori estimate for the error are obtained.
Keywords: Bessel operator, Kipriyanov spaces, difference scheme, Steklov averaging operator, strong solution 
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     title = {On strong solutions of a $B$-elliptic boundary-value problem and its difference approximation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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O. P. Barabash. On strong solutions of a $B$-elliptic boundary-value problem and its difference approximation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV", Voronezh, April 26-30, 2024, Part 2, Tome 236 (2024), pp. 3-12. http://geodesic.mathdoc.fr/item/INTO_2024_236_a0/