Some number-theoretic methods for solving partial derivatives
https://doi.org/10.22405/2226-8383-2021-22-3-256-297
Abstract
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.
About the Author
Alexander Valer’evich Rodionov
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
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For citations:
Rodionov A.V. Some number-theoretic methods for solving partial derivatives. Chebyshevskii Sbornik. 2021;22(3):256-297. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-3-256-297
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