Geodesic
Iterative identification of the diffusion coefficient in an initial boundary value problem for the subdiffusion equation
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 2, pp. 23-37

Voir la notice de l'article provenant de la source Math-Net.Ru

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, finite-difference method, iterative secant method.
Mots-clés : subdiffusion equation, inverse problem, identification of the diffusion coefficient 
@article{SJIM_2021_24_2_a1,
     author = {V. I. Vasil'ev and A. M. Kardashevsky},
     title = {Iterative identification of the diffusion coefficient in an initial boundary value problem for the subdiffusion equation},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {23--37},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2021_24_2_a1/}
}
TY  - JOUR
AU  - V. I. Vasil'ev
AU  - A. M. Kardashevsky
TI  - Iterative identification of the diffusion coefficient in an initial boundary value problem for the subdiffusion equation
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2021
SP  - 23
EP  - 37
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2021_24_2_a1/
LA  - ru
ID  - SJIM_2021_24_2_a1
ER  - 
%0 Journal Article
%A V. I. Vasil'ev
%A A. M. Kardashevsky
%T Iterative identification of the diffusion coefficient in an initial boundary value problem for the subdiffusion equation
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2021
%P 23-37
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2021_24_2_a1/
%G ru
%F SJIM_2021_24_2_a1
V. I. Vasil'ev; A. M. Kardashevsky. Iterative identification of the diffusion coefficient in an initial boundary value problem for the subdiffusion equation. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 2, pp. 23-37. http://geodesic.mathdoc.fr/item/SJIM_2021_24_2_a1/