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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2015, Volume 18, Number 3, Pages 327–335
DOI: https://doi.org/10.15372/SJNM20150307 (Mi sjvm585) 		 
This article is cited in 14 scientific papers (total in 14 papers)

A numerical solution of an inverse boundary value problem of heat conduction using the Volterra equations of the first kind

S. V. Solodushaa, N. M. Yaparovab

a Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences, 130 Lermontov str., Irkutsk, 664033, Russia
b South Ural State University, 76 Lenin pr., Chelyabinsk, 454080, Russia
Full-text PDF (417 kB) Citations (14)
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DOI: https://doi.org/10.15372/SJNM20150307
Abstract: We consider an inverse boundary value problem of heat conduction. To solve it, we propose a new approach based on the Laplace transform. This approach allows us to confine the original problem to solving the Volterra equations of the first kind. We have developed algorithms of the numerical solution to the resulting integral equations. The algorithms developed are based on the application of the product integration method and the quadrature of middle rectangles. A series of test calculations were performed to test the efficiency of the numerical methods.
Key words: Volterra integral equations, numerical solution, product integration method.
Received: 07.07.2014
Revised: 17.10.2014
English version:
Numerical Analysis and Applications, 2015, Volume 8, Issue 3, Pages 267–274
DOI: https://doi.org/10.1134/S1995423915030076
Bibliographic databases:
Document Type: Article
UDC: 519.642.5
Language: Russian
Citation: S. V. Solodusha, N. M. Yaparova, “A numerical solution of an inverse boundary value problem of heat conduction using the Volterra equations of the first kind”, Sib. Zh. Vychisl. Mat., 18:3 (2015), 327–335; Num. Anal. Appl., 8:3 (2015), 267–274
Citation in format AMSBIB
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\paper A numerical solution of an inverse boundary value problem of heat conduction using the Volterra equations of the first kind
\jour Sib. Zh. Vychisl. Mat.
\yr 2015
\vol 18
\issue 3
\pages 327--335
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\crossref{https://doi.org/10.15372/SJNM20150307}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3492617}
\elib{https://elibrary.ru/item.asp?id=23907304}
\transl
\jour Num. Anal. Appl.
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\pages 267--274
\crossref{https://doi.org/10.1134/S1995423915030076}
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  • https://www.mathnet.ru/eng/sjvm585
  • https://www.mathnet.ru/eng/sjvm/v18/i3/p327
    • This publication is cited in the following 14 articles:
    1. S. B. Sorokin, “Difference method for calculating the heat flux at an inaccessible boundary in the problem of heat conduction”, J. Appl. Industr. Math., 17:3 (2023), 651–663  mathnet  crossref  crossref
    2. Volodymyr Fedorchuk, Vitalii Ivaniuk, Vadym Ponedilok, 2022 IEEE 4th International Conference on Advanced Trends in Information Theory (ATIT), 2022, 19  crossref
    3. B.S. Ablabekov, A.T. Mukanbetova, “ON SOLVABILITY OF THE BOUNDARY INVERSE PROBLEM FOR THE HEAT CONDUCTIVITY EQUATION”, The herald of KSUCTA n.a.N.Isanov, 2021, no. 4-2021, 670  crossref
    4. Andriy Verlan, Volodymyr Fedorchuk, Vitalii Ivaniuk, Jo Sterten, Advances in Intelligent Systems and Computing, 1323, 11th World Conference “Intelligent System for Industrial Automation” (WCIS-2020), 2021, 18  crossref
    5. A. L. Karchevsky, “Numerical solving the heat equation with data on a time-like boundary for the heated thin foil technique”, Eurasian J. Math. Comput. Appl., 8:4 (2020), 4–14  crossref  mathscinet  isi  scopus
    6. Elena Tabarintseva, Communications in Computer and Information Science, 1090, Mathematical Optimization Theory and Operations Research, 2019, 578  crossref
    7. A. L. Karchevsky, “Development of the heated thin foil technique for investigating nonstationary transfer processes”, Interfacial Phenom. Heat Transf., 6:3 (2018), 179–185  crossref  isi  scopus
    8. E. V. Tabarintseva, “On approximate solution of inverse problem for nonlinear equation with discontinuous coefficient”, 2018 Global Smart Industry Conference (GloSIC), IEEE, 2018  crossref  isi
    9. N. M. Yaparova, A. D. Drozin, “Method for internal heat source identification in a rod based on indirect temperature measurements”, 2017 2nd International Ural Conference on Measurements (URALCON), IEEE, 2017, 93–98  crossref  isi
    10. E. V. Tabarintseva, “On approximate solution of non-linear inverse problem”, 2017 2nd International Ural Conference on Measurements (URALCON), IEEE, 2017, 99–106  crossref  isi
    11. S. V. Solodusha, I. V. Mokry, “A numerical solution of one class of Volterra integral equations of the first kind in terms of the machine arithmetic features”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:3 (2016), 119–129  mathnet  crossref  elib
    12. N. M. Yaparova, “Chislennyi metod resheniya obratnoi zadachi s neizvestnymi nachalnymi usloviyami dlya nelineinogo parabolicheskogo uravneniya”, Vestn. YuUrGU. Ser. Vych. matem. inform., 5:2 (2016), 43–58  mathnet  crossref  elib
    13. N. M. Yaparova, “Metod resheniya obratnoi zadachi identifikatsii funktsii istochnika s ispolzovaniem preobrazovaniya Laplasa”, Vestn. YuUrGU. Ser. Vych. matem. inform., 5:3 (2016), 20–35  mathnet  crossref  elib
    14. M. Joachimiak, A. Frackowiak, M. Cialkowski, “Solution of inverse heat conduction equation with the use of Chebyshev polynomials”, Arch. Thermodyn., 37:4 (2016), 73–88  crossref  isi
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