Geodesic
Some number-theoretic methods for solving partial derivatives
Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 256-297

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, a new method is constructed for solving partial differential equations using a sequence of nested generalized parallelepiped grids. This method is a generalization and development of the V. S. Ryaben'kii and N. M. Korobov method for the approximate solution of partial differential equations for the case of using arbitrary generalized parallelepiped grids for integer lattices. The error of this method was also found. In the case of using an infinite sequence of nested generalized parallelepiped grids, a fairly fast convergence will take place. In addition, a variant of constructing optimal grids in the two-dimensional case is proposed. It is based on the integer approximation of algebraic lattices. In the two-dimensional case, the grids constructed in this way will always give generalized parallelepiped grids. Moreover, there are simple ways to assess the quality of the resulting meshes. One such method, based on the use of a hyperbolic parameter, is considered in this paper.
Keywords: finite fields, squares, sums. 
@article{CHEB_2021_22_3_a16,
     author = {A. V. Rodionov},
     title = {Some number-theoretic methods for solving partial derivatives},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {256--297},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a16/}
}
TY  - JOUR
AU  - A. V. Rodionov
TI  - Some number-theoretic methods for solving partial derivatives
JO  - Čebyševskij sbornik
PY  - 2021
SP  - 256
EP  - 297
VL  - 22
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a16/
LA  - ru
ID  - CHEB_2021_22_3_a16
ER  - 
%0 Journal Article
%A A. V. Rodionov
%T Some number-theoretic methods for solving partial derivatives
%J Čebyševskij sbornik
%D 2021
%P 256-297
%V 22
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a16/
%G ru
%F CHEB_2021_22_3_a16
A. V. Rodionov. Some number-theoretic methods for solving partial derivatives. Čebyševskij sbornik, Tome 22 (2021) no. 3, pp. 256-297. http://geodesic.mathdoc.fr/item/CHEB_2021_22_3_a16/