Standard

Numerical Algorithm for Source Determination in a Diffusion–Logistic Model from Integral Data Based on Tensor Optimization. / Zvonareva, T. A.; Kabanikhin, S. I.; Krivorotko, O. I.

в: Computational Mathematics and Mathematical Physics, Том 63, № 9, 09.2023, стр. 1654-1663.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Zvonareva, TA, Kabanikhin, SI & Krivorotko, OI 2023, 'Numerical Algorithm for Source Determination in a Diffusion–Logistic Model from Integral Data Based on Tensor Optimization', Computational Mathematics and Mathematical Physics, Том. 63, № 9, стр. 1654-1663. https://doi.org/10.1134/S0965542523090166

APA

Zvonareva, T. A., Kabanikhin, S. I., & Krivorotko, O. I. (2023). Numerical Algorithm for Source Determination in a Diffusion–Logistic Model from Integral Data Based on Tensor Optimization. Computational Mathematics and Mathematical Physics, 63(9), 1654-1663. https://doi.org/10.1134/S0965542523090166

Vancouver

Zvonareva TA, Kabanikhin SI, Krivorotko OI. Numerical Algorithm for Source Determination in a Diffusion–Logistic Model from Integral Data Based on Tensor Optimization. Computational Mathematics and Mathematical Physics. 2023 сент.;63(9):1654-1663. doi: 10.1134/S0965542523090166

Author

Zvonareva, T. A. ; Kabanikhin, S. I. ; Krivorotko, O. I. / Numerical Algorithm for Source Determination in a Diffusion–Logistic Model from Integral Data Based on Tensor Optimization. в: Computational Mathematics and Mathematical Physics. 2023 ; Том 63, № 9. стр. 1654-1663.

BibTeX

@article{2cf0c3fa20a84cc8a2926b89eca77d3b,
title = "Numerical Algorithm for Source Determination in a Diffusion–Logistic Model from Integral Data Based on Tensor Optimization",
abstract = "An algorithm has been developed for numerically solving the source determination problem in the model of information dissemination in synthetic online social networks, described by reaction–diffusion-type equations, using additional information about the process at fixed time points. The degree of ill-posedness of the source determination problem for a parabolic equation is studied based on the analysis of singular values of the linearized operator of the inverse problem. The algorithm developed is based on a combination of the tensor optimization method and gradient descent supplemented with the A.N. Tikhonov regularization. Numerical calculations demonstrate the smallest relative error in the reconstructed source obtained by the developed algorithm in comparison with classical approaches.",
keywords = "gradient methods, inverse problem, reaction–diffusion model, regularization, source determination problem, tensor optimization",
author = "Zvonareva, {T. A.} and Kabanikhin, {S. I.} and Krivorotko, {O. I.}",
note = "This work was supported by the Russian Science Foundation (project no. 18-71-10044-P) and the Mathematical Center in Akademgorodok (agreement with the Ministry of Science and Higher Education of the Russian Federation no. 075-15-2022-281). Публикация для корректировки.",
year = "2023",
month = sep,
doi = "10.1134/S0965542523090166",
language = "English",
volume = "63",
pages = "1654--1663",
journal = "Computational Mathematics and Mathematical Physics",
issn = "0965-5425",
publisher = "PLEIADES PUBLISHING INC",
number = "9",

}

RIS

TY - JOUR

T1 - Numerical Algorithm for Source Determination in a Diffusion–Logistic Model from Integral Data Based on Tensor Optimization

AU - Zvonareva, T. A.

AU - Kabanikhin, S. I.

AU - Krivorotko, O. I.

N1 - This work was supported by the Russian Science Foundation (project no. 18-71-10044-P) and the Mathematical Center in Akademgorodok (agreement with the Ministry of Science and Higher Education of the Russian Federation no. 075-15-2022-281). Публикация для корректировки.

PY - 2023/9

Y1 - 2023/9

N2 - An algorithm has been developed for numerically solving the source determination problem in the model of information dissemination in synthetic online social networks, described by reaction–diffusion-type equations, using additional information about the process at fixed time points. The degree of ill-posedness of the source determination problem for a parabolic equation is studied based on the analysis of singular values of the linearized operator of the inverse problem. The algorithm developed is based on a combination of the tensor optimization method and gradient descent supplemented with the A.N. Tikhonov regularization. Numerical calculations demonstrate the smallest relative error in the reconstructed source obtained by the developed algorithm in comparison with classical approaches.

AB - An algorithm has been developed for numerically solving the source determination problem in the model of information dissemination in synthetic online social networks, described by reaction–diffusion-type equations, using additional information about the process at fixed time points. The degree of ill-posedness of the source determination problem for a parabolic equation is studied based on the analysis of singular values of the linearized operator of the inverse problem. The algorithm developed is based on a combination of the tensor optimization method and gradient descent supplemented with the A.N. Tikhonov regularization. Numerical calculations demonstrate the smallest relative error in the reconstructed source obtained by the developed algorithm in comparison with classical approaches.

KW - gradient methods

KW - inverse problem

KW - reaction–diffusion model

KW - regularization

KW - source determination problem

KW - tensor optimization

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85174278544&origin=inward&txGid=e3d0e1a1eb6627a2b9320aa9d190ed00

UR - https://www.mendeley.com/catalogue/70f464d9-0c49-3e0e-9631-2f9ecf4794d7/

U2 - 10.1134/S0965542523090166

DO - 10.1134/S0965542523090166

M3 - Article

VL - 63

SP - 1654

EP - 1663

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 9

ER -

ID: 59265442