Geodesic
Iterative solution of the retrospective inverse heat conduction problem using the Poisson integral
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 72-85

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This paper considers the inverse problem of identification of the finite initial condition of the Cauchy problem for the homogeneous heat conduction equation using the first kind linear Fredholm integral equation. Its discretization is carried out with the help of the quadrature rectangular formula. For the numerical realization of the obtained system of linear algebraic equations with almost complete, symmetric, positively determined, ill-conditioned matrix it is proposed to use the method of conjugate gradients. Examples of reconstruction of smooth, nonsmooth and discontinuous initial conditions in one- and two-dimensional cases, including the introduction of «noise», characteristic of redefinition conditions of inverse problems, are given.
Keywords: retrospective inverse heat conduction problem, first kind Fredholm integral equation, system of linear equations with ill-conditioned matrix, method of conjugate gradients.
Mots-clés : Poisson integral 
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     title = {Iterative solution of the retrospective inverse heat conduction problem using the {Poisson} integral},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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V. I. Vasiliev; A. M. Kardashevsky. Iterative solution of the retrospective inverse heat conduction problem using the Poisson integral. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 72-85. http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a23/