Geodesic
Numerical solution to inverse problems for linear parabolic equation
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2018), pp. 69-87

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In the paper, the inverse problems for a parabolic equation with unknown coefficients on the right-hand side are considered. Boundary value problems with nonlocal conditions are reduced to such problems. We investigate separately two cases: unknown coefficients depend on either time variable only or phase coordinates only. A numerical method to solve the problems by using the method of lines is suggested. The results of numerical experiments on test problems are given.
Keywords: inverse problem, method of lines, parametric identification.
Mots-clés : nonlocal conditions, parabolic equation 
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     author = {A. B. Ragimov},
     title = {Numerical solution to inverse problems for linear parabolic equation},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {69--87},
     publisher = {mathdoc},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2018_1_a5/}
}
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A. B. Ragimov. Numerical solution to inverse problems for linear parabolic equation. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2018), pp. 69-87. http://geodesic.mathdoc.fr/item/VTPMK_2018_1_a5/