Geodesic
A local one-dimensional scheme for parabolic equation of general form, describing microphysical processes in convective clouds
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2018), pp. 158-167

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This paper considers a locally one-dimensional scheme for a parabolic equation of general form in a p-dimensional parallelepiped.To describe coagulation processes in the cloud, the equation under study involves a non-local source of a specific type [1]. An a priori estimate for the solution to the locally one-dimensional scheme is obtained and its convergence is proved. Sign definiteness for the operator in the principal part of the equation is not assumed.
Keywords: boundary value problem, locally one-dimensional scheme, stability, approximation error.
Mots-clés : scheme convergence 
@article{VKAM_2018_3_a18,
     author = {B. A. Ashabokov and I. D. Taisaev and M. H. Shhanukov-Lafishev},
     title = {A local one-dimensional scheme for parabolic equation of general form, describing microphysical processes in convective clouds},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {158--167},
     publisher = {mathdoc},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2018_3_a18/}
}
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B. A. Ashabokov; I. D. Taisaev; M. H. Shhanukov-Lafishev. A local one-dimensional scheme for parabolic equation of general form, describing microphysical processes in convective clouds. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2018), pp. 158-167. http://geodesic.mathdoc.fr/item/VKAM_2018_3_a18/