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Cybernetics and Systems Analysis

, Volume 55, Issue 6, pp 988–998 | Cite as

A Splitting Scheme for Diffusion and Heat Conduction Problems

  • A. V. GladkyEmail author
  • Y. A. Gladka
Article
  • 3 Downloads

Abstract

The problem of mathematical modeling and optimization of nonstationary diffusion and heat conduction processes is considered. An approach that uses the idea of splitting and computation of the obtained difference schemes using explicit schemes of point to point computing is proposed for numerical solution of multidimensional diffusion and heat conduction initial–boundary-value problems. Construction of difference splitting schemes, approximation and stability on 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 finding the optimal control is proposed.

Keywords

parabolic equation optimal control problem numerical method splitting methods difference scheme stability 

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.Kyiv National Economic University Named after Vadym HetmanKyivUkraine

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