Klyachin A.A., Klyachin V.A. The Approximation of the Fourth-Order Partial Differential Equations in the Class of the Piecewise Polynomial Functions on the Triangular Grid

https://doi.org/10.15688/mpcm.jvolsu.2019.2.5

Aleksey Aleksandrovich Klyachin
Doctor of Physical and Mathematical Sciences,
Head of the Department of Mathematical Analysis and Function Theory,
Volgograd State University
This email address is being protected from spambots. You need JavaScript enabled to view it. , This email address is being protected from spambots. You need JavaScript enabled to view it.
https://orcid.org/0000-0003-3293-9066
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Vladimir Aleksandrovich Klyachin
Doctor of Physical and Mathematical Sciences,
Head of the Department of Computer Sciences and Experimental Mathematics,
Volgograd State University
This email address is being protected from spambots. You need JavaScript enabled to view it. , This email address is being protected from spambots. You need JavaScript enabled to view it.
https://orcid.org/0000-0003-1922-7849
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. The present work determines the deviation of the piecewise cubic almost-solution of the biharmonic equation and derives the general formula (3) for its calculation. Based on this concept, we obtained an approximation of the equation. A number of numerical calculations were carried out in order to confirm the obtained formula (see pictures 1 and 2) experimentally. In general, for all selected biharmonic functions, the deviation value εΔΔ(u) turned out to be, as expected, rather small even with a relatively small number of triangulation nodes. On average, with 25 ≤ N ≤ 35, the absolute error was about 0,0001, which gives an approximately asymptotic estimate of O(h2) when the partitioning step is h→0.

Key words: piecewise cubic function, almost solution, biharmonic equation, approximation of the equation, deviation of the piecewise cubic almost solution.

Creative Commons License
The Approximation of the Fourth-Order Partial Differential  Equations in the Class of the Piecewise Polynomial Functions on the Triangular Grid by Klyachin A.A., Klyachin V.A. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 22 No. 2 2019, pp. 65-72

Attachments:
Download this file (5. Klyachin, Klyachin.pdf) 5. Klyachin, Klyachin.pdf
URL: https://mp.jvolsu.com/index.php/en/component/attachments/download/866
471 Downloads