Numerical Algorithm for Source Determination in a Diffusion–Logistic Model from Integral Data Based on Tensor Optimization Full article
| Journal |
Computational Mathematics and Mathematical Physics
ISSN: 0965-5425 , E-ISSN: 1555-6662 |
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| Output data | Year: 2023, Volume: 63, Number: 9, Pages: 1654–1663 Pages count : 10 DOI: 10.1134/S0965542523090166 | ||||||
| Tags | source determination problem, reaction–diffusion model, inverse problem, tensor optimization, regularization, gradient methods | ||||||
| Authors |
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| Affiliations |
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Funding (2)
| 1 |
Министерство науки и высшего образования РФ Mathematical Center in Akademgorodok |
075-15-2019-1613, 075-15-2022-281 |
| 2 | Russian Science Foundation | 18-71-10044-P |
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 reactiondiffusion-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.
Cite:
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
Computational Mathematics and Mathematical Physics. 2023. V.63. N9. P.1654–1663. DOI: 10.1134/S0965542523090166 WOS Scopus РИНЦ OpenAlex
Numerical Algorithm for Source Determination in a Diffusion–Logistic Model from Integral Data Based on Tensor Optimization
Computational Mathematics and Mathematical Physics. 2023. V.63. N9. P.1654–1663. DOI: 10.1134/S0965542523090166 WOS Scopus РИНЦ OpenAlex
Original:
Звонарева Т.А.
, Кабанихин С.И.
, Криворотько О.И.
Численный алгоритм определения источника диффузионно-логистической модели по данным интегрального типа, основанный на тензорной оптимизации
Журнал вычислительной математики и математической физики. 2023. Т.63. №9. С.1513-1523. DOI: 10.31857/S0044466923090193 РИНЦ MathNet OpenAlex
Численный алгоритм определения источника диффузионно-логистической модели по данным интегрального типа, основанный на тензорной оптимизации
Журнал вычислительной математики и математической физики. 2023. Т.63. №9. С.1513-1523. DOI: 10.31857/S0044466923090193 РИНЦ MathNet OpenAlex
Dates:
| Submitted: | Sep 9, 2022 |
| Accepted: | May 29, 2023 |
| Published print: | Oct 13, 2023 |
| Published online: | Oct 13, 2023 |
Identifiers:
| Web of science: | WOS:001086856200006 |
| Scopus: | 2-s2.0-85174278544 |
| Elibrary: | 63490447 |
| OpenAlex: | W4387620262 |