This article is cited in 1 paper

NUMERICAL METHODS AND THE BASIS FOR THEIR APPLICATION

Adjoint grid parabolic quazilinear boundaryvalue problems

I. A. Chernov^a, S. V. Manicheva<sup>b

a</sup> Institute of Applied Math Research, 11 Pushkinskaya street, Petrozavodsk, 185910, Russia
^b Karelian State Pedagogical Academy, 17 Pushkinskaya street, Petrozavodsk, 185035, Russia

Abstract: 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.

UDC: 517.954

Received: 30.01.2012

DOI: 10.20537/2076-7633-2012-4-2-275-291