Numerical Method for the Inverse Boundary-Value Problem of the Heat Equation

The article considers the inverse boundary-value problem of heat conduction which involves determining the time distribution of temperature on the boundary given the spatial distribution of the temperature at the final time instant. The problem is reduced to an integral equation of the first kind wi...

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Bibliographic Details
Published in:Computational mathematics and modeling Vol. 28; no. 2; pp. 141 - 147
Main Authors: Dmitriev, V. I., Stolyarov, L. V.
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2017
Springer Nature B.V
Subjects:
Applications of Mathematics
Boundary value problems
Computational Mathematics and Numerical Analysis
Conduction heating
Conductive heat transfer
I. Inverse Problems
Integral equations
Iterative methods
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Numerical methods
Optimization
Spatial distribution
Thermodynamics
boundary-value problem for the heat equation
method for solving inverse problems
inverse problems
ISSN:1046-283X, 1573-837X
Online Access:Get full text
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Summary:The article considers the inverse boundary-value problem of heat conduction which involves determining the time distribution of temperature on the boundary given the spatial distribution of the temperature at the final time instant. The problem is reduced to an integral equation of the first kind with a symmetrical kernel. The integral equation is solved by a special iterative method. Test examples demonstrate convergence and stability of the proposed method.
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ISSN:1046-283X
1573-837X
DOI:10.1007/s10598-017-9352-7