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.
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Original Russian Text © P.N. Vabishchevich, V.I. Vasil’ev, M.V. Vasil’eva, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 6, pp. 1020–1027.
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Vabishchevich, P.N., Vasil’ev, V.I. & Vasil’eva, M.V. Computational identification of the right-hand side of a parabolic equation. Comput. Math. and Math. Phys. 55, 1015–1021 (2015). https://doi.org/10.1134/S0965542515030185
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DOI: https://doi.org/10.1134/S0965542515030185