Geodesic
Numerical solution of the retrospective inverse problem of heat conduction with the help of the Poisson integral
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 3, pp. 26-36

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We consider the retrospective inverse problem that consists in determining the initial solution of the one-dimensional heat conduction equation with a given condition at the final instant of time. The solution of the problem is given in the form of the Poisson integral and is numerically realized by means of a quadrature formula leading to a system of linear algebraic equations with dense matrix. The results of numerical experiments are presented and show the efficiency of the numerical method including the case of the final condition with random errors.
Keywords: heat conduction equation, retrospective inverse problem of heat conduction, integral equation, numerical method, system of linear equations, random errors.
Mots-clés : Poisson integral 
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     author = {V. I. Vasil'ev and A. M. Kardashevskii},
     title = {Numerical solution of the retrospective inverse problem of heat conduction with the help of the {Poisson} integral},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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     publisher = {mathdoc},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_3_a2/}
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V. I. Vasil'ev; A. M. Kardashevskii. Numerical solution of the retrospective inverse problem of heat conduction with the help of the Poisson integral. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 3, pp. 26-36. http://geodesic.mathdoc.fr/item/SJIM_2018_21_3_a2/