Numerical Solution of the Retrospective Inverse Problem of Heat Conduction with the Help of the Poisson Integral
- Authors: Vasil’ev V.I.1, Kardashevskii A.M.1
-
Affiliations:
- Ammosov North-Eastern Federal University
- Issue: Vol 12, No 3 (2018)
- Pages: 577-586
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213102
- DOI: https://doi.org/10.1134/S1990478918030158
- ID: 213102
Cite item
Abstract
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.
About the authors
V. I. Vasil’ev
Ammosov North-Eastern Federal University
Author for correspondence.
Email: vasvasil@mail.ru
Russian Federation, ul. Belinskogo 58, Yakutsk, 677000
A. M. Kardashevskii
Ammosov North-Eastern Federal University
Email: vasvasil@mail.ru
Russian Federation, ul. Belinskogo 58, Yakutsk, 677000