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The discrete, fractional order model of a two-dimensional temperature field using Grünwald-Letnikov definition.

Authors :
OPRZĘDKIEWICZ, Krzysztof
Source :
Bulletin of the Polish Academy of Sciences: Technical Sciences. Jul2024, Vol. 72 Issue 4, p1-13. 13p.
Publication Year :
2024

Abstract

In the paper a new, fractional order, discrete model of a two-dimensional temperature field is addressed. The proposed model uses Grünwald-Letnikov definition of the fractional operator. Such a model has not been proposed yet. Elementary properties of the model: practical stability, accuracy and convergence are analysed. Analytical conditions of stability and convergence are proposed and they allow us to estimate the orders of the model. Theoretical considerations are validated using experimental data obtained with the use of a thermal imaging camera. Results of analysis supported by experiments point that the proposed model assures good accuracy and convergence for low order and relatively short memory length. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02397528
Volume :
72
Issue :
4
Database :
Academic Search Index
Journal :
Bulletin of the Polish Academy of Sciences: Technical Sciences
Publication Type :
Academic Journal
Accession number :
178470678
Full Text :
https://doi.org/10.24425/bpasts.2024.150332