Geodesic
Computational identification of the right-hand side of a parabolic equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 1020-1027 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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P. N. Vabishchevich; V. l. Vasil'ev; M. V. Vasil'eva. Computational identification of the right-hand side of a parabolic equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 6, pp. 1020-1027. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_6_a9/

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