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REPORTS BY YOUNG SCIENTISTS
Some number-theoretic methods for solving partial derivatives
A. V. Rodionov Tula State Lev Tolstoy Pedagogical University (Tula)
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.
Keywords:
finite fields, squares, sums.
Received: 24.05.2021 Accepted: 20.09.2021
Citation:
A. V. Rodionov, “Some number-theoretic methods for solving partial derivatives”, Chebyshevskii Sb., 22:3 (2021), 256–297
Linking options:
https://www.mathnet.ru/eng/cheb1074 https://www.mathnet.ru/eng/cheb/v22/i3/p256
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Abstract page: | 128 | Full-text PDF : | 43 | References: | 17 |
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