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This article is cited in 31 scientific papers (total in 31 papers)
Computational identification of the right-hand side of a parabolic equation
P. N. Vabishchevicha, V. l. Vasil'evb, M. V. Vasil'evab a Nuclear Safety Institute, Russian Academy of Sciences, ul. Bol’shaya Tul’skaya 52, Moscow, 115191, Russia
b Ammosov North-Eastern Federal University, ul. Belinskogo 58, Yakutsk, 677000, Russia
Abstract:
Among inverse problems for partial differential equations, a task of interest is to study coefficient inverse problems related to identifying the right-hand side of an equation with the use of additional information. In the case of nonstationary problems, finding the dependence of the right-hand side on time and the dependence of the right-hand side on spatial variables can be treated as independent tasks. These inverse problems are linear, which considerably simplifies their study. The time dependence of the right-hand side of a multidimensional parabolic equation is determined using an additional solution value at a point of the computational domain. The inverse problem for a model equation in a rectangle is solved numerically using standard spatial difference approximations. The numerical algorithm relies on a special decomposition of the solution whereby the transition to a new time level is implemented by solving two standard grid elliptic problems. Numerical results are presented.
Key words:
inverse problems, identification of coefficients, parabolic equation, difference schemes.
Received: 11.08.2014
Citation:
P. N. Vabishchevich, V. l. Vasil'ev, M. V. Vasil'eva, “Computational identification of the right-hand side of a parabolic equation”, Zh. Vychisl. Mat. Mat. Fiz., 55:6 (2015), 1020–1027; Comput. Math. Math. Phys., 55:6 (2015), 1015–1021
Linking options:
https://www.mathnet.ru/eng/zvmmf10223 https://www.mathnet.ru/eng/zvmmf/v55/i6/p1020
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