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.
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2019, pp. 122–133.
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Gladky, A.V., Gladka, Y.A. A Splitting Scheme for Diffusion and Heat Conduction Problems. Cybern Syst Anal 55, 988–998 (2019). https://doi.org/10.1007/s10559-019-00209-5
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DOI: https://doi.org/10.1007/s10559-019-00209-5