Abstract:
We propose an iterative solution method for an implicit finite-difference analog of the inverse problem of identifying the diffusion coefficient in an initial boundary value problem for the subdiffusion equation with the fractional Caputo time derivative.
We consider the two different ways of setting the overdetermination condition at the final time point: the value of the solution at some given point and a weighted integral of the solution.
The results of numerical implementation of the iterative method are presented on model problems with exact solutions. These results confirm the sufficiently high accuracy of the method.
Keywords:
Caputo fractional time derivative, subdiffusion equation,
inverse problem, finite-difference method, identification of the diffusion coefficient, iterative secant method.
Citation:
V. I. Vasil'ev, A. M. Kardashevsky, “Iterative identification of the diffusion coefficient in an initial boundary value problem for the subdiffusion equation”, Sib. Zh. Ind. Mat., 24:2 (2021), 23–37; J. Appl. Industr. Math., 15:2 (2021), 343–354
\Bibitem{VasKar21}
\by V.~I.~Vasil'ev, A.~M.~Kardashevsky
\paper Iterative identification of the diffusion coefficient in an initial boundary value problem for the subdiffusion equation
\jour Sib. Zh. Ind. Mat.
\yr 2021
\vol 24
\issue 2
\pages 23--37
\mathnet{http://mi.mathnet.ru/sjim1127}
\crossref{https://doi.org/10.33048/SIBJIM.2021.24.202}
\elib{https://elibrary.ru/item.asp?id=47508376}
\transl
\jour J. Appl. Industr. Math.
\yr 2021
\vol 15
\issue 2
\pages 343--354
\crossref{https://doi.org/10.1134/S1990478921020162}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85116275761}
Linking options:
https://www.mathnet.ru/eng/sjim1127
https://www.mathnet.ru/eng/sjim/v24/i2/p23
This publication is cited in the following 2 articles:
Anatoly Alikhanov, Huiran Bai, Jian Huang, Aleksei Tyrylgin, Yin Yang, “Multiscale model reduction for the time fractional thermoporoelasticity problem in fractured and heterogeneous media”, Journal of Computational and Applied Mathematics, 2024, 116157
Aleksei Tyrylgin, Maria Vasilyeva, Anatoly Alikhanov, Dongwoo Sheen, “A computational macroscale model for the time fractional poroelasticity problem in fractured and heterogeneous media”, Journal of Computational and Applied Mathematics, 418 (2023), 114670
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