Adjoint grid parabolic quazilinear boundary-value problems

Chernov I.A., Manicheva S.V.
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In the paper we construct the adjoint problem for the explicit and implicit parabolic quazi-linear grid boundary-value problems with one spatial variable; the coefficients of the problems depend on the solution at the same time and earlier times. Dependence on the history of the solution is via the state vector; its evolution is described by the differential equation. Many models of diffusion mass transport are reduced to such boundary-value problems. Having solutions to the direct and adjoint problems, one can obtain the exact value of the gradient of a functional in the space of parameters the problem also depends on. We present solving algorithms, including the parallel one.

Keywords: adjoint problem, evaluation of parameters, mathematical modelling, gradient methods
Citation in English: Chernov I.A., Manicheva S.V. Adjoint grid parabolic quazilinear boundary-value problems // Computer Research and Modeling, 2012, vol. 4, no. 2, pp. 275-291
Citation in English: Chernov I.A., Manicheva S.V. Adjoint grid parabolic quazilinear boundary-value problems // Computer Research and Modeling, 2012, vol. 4, no. 2, pp. 275-291
DOI: 10.20537/2076-7633-2012-4-2-275-291
URL: http://crm-en.ics.org.ru/journal/article/1888/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.
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