Geodesic
Locally one-dimensional schemes for an equation describing coagulation processes in convective clouds with ``memory''
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 39 (2022) no. 2, pp. 184-196

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The paper considers a locally one-dimensional difference scheme for a general parabolic equation in a p-dimensional parallelepiped. To describe coagulation processes in media with “memory”, non-local sources of a special type are included in the equation. An a priori estimate is obtained for solving the corresponding difference scheme, which implies its convergence.
Keywords: boundary value problem, locally one-dimensional difference scheme, stability and convergence of the difference scheme, approximation error. 
@article{VKAM_2022_39_2_a12,
     author = {M. Kh. Shkhanukov-Lafishev and M. M. Lafisheva and I. D. Taisaev},
     title = {Locally one-dimensional schemes for an equation describing coagulation processes in convective clouds with ``memory''},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {184--196},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2022_39_2_a12/}
}
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M. Kh. Shkhanukov-Lafishev; M. M. Lafisheva; I. D. Taisaev. Locally one-dimensional schemes for an equation describing coagulation processes in convective clouds with ``memory''. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 39 (2022) no. 2, pp. 184-196. http://geodesic.mathdoc.fr/item/VKAM_2022_39_2_a12/