Abstract
We consider a retrospective inverse heat conduction problem with nonstationary inhomogeneous Dirichlet boundary conditions. It is approximated by a Crank–Nicolson scheme that has the second order of approximation both in the spatial variable and in time. It is proposed to use the iterative method of conjugate gradients to determine the solution of the resulting system of linear algebraic equations. Examples are given of reconstructing smooth, nonsmooth, and discontinuous initial conditions, including the introduction of a “noise” characteristic, typical of additional conditions of inverse problems, and its smoothing using the Savitzky–Golay filter.
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The work was carried out within the framework of the state order, project no. FSRG-2021-0015.
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Translated by V. Potapchouck
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Vasil’ev, V.I., Kardashevsky, A.M. & Popov, V.V. Iterative Solution of a Retrospective Inverse Heat Conduction Problem with Inhomogeneous Dirichlet Boundary Conditions. J. Appl. Ind. Math. 16, 841–852 (2022). https://doi.org/10.1134/S1990478922040238
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DOI: https://doi.org/10.1134/S1990478922040238