Finite-difference operators for 2D problems
Authors:
- T.J. Sobczyk
Abstract
This paper presents the concept of using algorithms for reducing the dimensions of finite-difference equations of two-dimensional (2D) problems, for second-order partial differential equations. Solutions are predicted as two-variable functions over the rectangular domain, which are periodic with respect to each variable and which repeat outside the domain. Novel finite-difference operators, of both the first and second orders, are developed for such functions. These operators relate the value of derivatives at each point to the values of the function at all points distributed uniformly over the function domain. A specific feature of the novel operators follows from the arrangement of the function values as well as the values of derivatives, which are rectangular matrices instead of vectors. This significantly reduces the dimensions of the finite-difference operators to the numbers of points in each direction of the 2D area. The finite-difference equations are created exemplary for elliptic equations. An original iterative algorithm is proposed for reducing the process of solving finite-difference equations to the multiplication of matrices.
- Record ID
- CUTc51a86913f334123b749d16d7a545f92
- Publication categories
- ;
- Author
- Journal series
- Bulletin of the Polish Academy of Sciences, Technical Sciences, ISSN 0239-7528, e-ISSN 2300-1917
- Issue year
- 2020
- Vol
- 68
- No
- 6
- Pages
- 1535-1541
- Other elements of collation
- Bibliografia (na s.) - 1540-1541; Bibliografia (liczba pozycji) - 19; Oznaczenie streszczenia - Abstr.; Numeracja w czasopiśmie - Vol. 68, No. 6
- Keywords in English
- second-order partial differential equations, 2D finite-difference operators, finite-difference equations, iterative algorithms
- DOI
- DOI:10.24425/bpasts.2020.135387 Opening in a new tab
- URL
- https://journals.pan.pl/bpasts/131826 Opening in a new tab
- Language
- eng (en) English
- License
- Score (nominal)
- 100
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUTc51a86913f334123b749d16d7a545f92/
- URN
urn:pkr-prod:CUTc51a86913f334123b749d16d7a545f92
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.