Geodesic
Application of the projection-grid method for solving nonstationary problems
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—XXXIV", Voronezh, May 3-9, 2023, Part 3, Tome 232 (2024), pp. 3-12

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The work is devoted to constructing approximate solutions of a parabolic differential equation with the Bessel operator. Solutions are sought in the form of a linear combination of piecewise continuous, compactly supported basis functions. The construction of the solution is performed in two stages. Initially, the approximation in a spatial variable is performed by using the Bubnov–Galerkin projection-grid method. Then the approximation in $t$ is carried out by using the finite-difference method. The resulting system of equations is solved by the tridiagonal matrix algorithm.
Keywords: Bessel operator, Bubnov–Galerkin method, finite functions, projection-grid method, finite-difference method 
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     title = {Application of the projection-grid method for solving nonstationary problems},
     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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     volume = {232},
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O. P. Barabash. Application of the projection-grid method for solving nonstationary problems. 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—XXXIV", Voronezh, May 3-9, 2023, Part 3, Tome 232 (2024), pp. 3-12. http://geodesic.mathdoc.fr/item/INTO_2024_232_a0/