Numerical Solution of the Retrospective Inverse Problem of Heat Conduction with the Help of the Poisson Integral

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...

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Bibliographic Details
Published in:Journal of applied and industrial mathematics 2018-07, Vol.12 (3), p.577-586
Main Authors: Vasil’ev, V. I., Kardashevskii, A. M.
Format: Article
Language:English
Subjects:
Conduction heating
Conductive heat transfer
Integrals
Inverse problems
Linear algebra
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrix methods
Numerical methods
Random errors
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Summary: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.
ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478918030158