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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 517:519.6
A.V. Gladky1, Y.A. Gladka2


1 V.M. Glushkov Institute of Cybernetics, National Academy
of Sciences of Ukraine, Kyiv, Ukraine

gladky@ukr.net

2 Kyiv National Economic University named after Vadym
Hetman, Kyiv, Ukraine

yuliyagladkaya@hotmail.com

ABOUT ONE SPLITTING SCHEME FOR DIFFUSION AND HEAT CONDUCTION PROBLEMS

Abstract. The problem of mathematical modeling and optimization of diffusion and heat conduction non-stationary processes is considered. An approach that uses the idea of splitting and computation of the obtained difference schemes using explicit schemes of running counting is proposed for the numerical solution of multidimensional diffusion and heat conduction initial-boundary-value problems. Construction of difference splitting schemes and approximation and stability on the initial data are investigated. Differential properties of the quality functional are analyzed for the numerical solution of the optimal control problem for a parabolic equation. An iterative algorithm for determining the optimal control is proposed.

Keywords: parabolic equation, optimal control problem, numerical method, splitting methods, difference scheme, stability.



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