Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Seregina E. V., Stepovich M. A. On the projection method for solving the heat equation with lumped heat capacity. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2025, vol. 25, iss. 2, pp. 173-183. DOI: 10.18500/1816-9791-2025-25-2-173-183, EDN: ERHSOY

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.05.2025
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Language: 
Russian
Heading: 
Mathematics
Article type: 
Article
UDC: 
517.95,519.63,51–73
DOI: 
10.18500/1816-9791-2025-25-2-173-183
EDN: 
ERHSOY

On the projection method for solving the heat equation with lumped heat capacity

Autors: 
Seregina Elena V., Bauman Moscow State Technical University (Kaluga Branch)
Stepovich Mikhail Adol'fovich, Kaluga State University named after K. E. Tsiolkovski
Abstract: 

This paper presents some results of the possibility of using the least squares projection method for solving heat equations with concentrated heat capacity on a half-line. An order estimate of the error is given of the considered projection scheme corresponding to an approximate solution of the heat equation using a basis of Laguerre – Jacobi polynomials. The results of calculations for a two-dimensional model problem are presented.

Key words: 
heat equation
lumped heat capacity
least squares projection method
Laguerre – Jacobi polynomials
modulus of continuity
Acknowledgments: 
This work was supported by the grant of the Russian Science Foundation and the Government of Kaluga Region (project No. 23-21-10069, https://rscf.ru/en/project/23-21-10069/).
References: 
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Received: 
25.02.2024
Accepted: 
21.10.2024
Published: 
30.05.2025
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