An Inverse Problem for the Heat Conduction Equation, III

1982 ◽  
Vol 108 (1) ◽  
pp. 73-78
Author(s):  
Gottfried Anger ◽  
Regine Czerner
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Conduction Equation

scholarly journals Analytical-numerical solution of the inverse problem for the heat conduction equation

2012 ◽  
Vol 7 (3) ◽  
pp. 239-253
Author(s):  
Michał Ciałkowski ◽  
Andrzej Maćkiewicz ◽  
Jan Kołodziej ◽  
Uwe Gampe ◽  
Andrzej Frąckowiak
Keyword(s):  
Inverse Problem ◽  
Heat Conduction ◽  
Numerical Solution ◽  
Heat Conduction Equation ◽  
Conduction Equation

scholarly journals Reconstruction of the thermal conductivity coefficient in the space fractional heat conduction equation

2017 ◽  
Vol 21 (1 Part A) ◽  
pp. 81-88 ◽  
Author(s):  
Rafał Brociek ◽  
Damian Słota
Keyword(s):  
Thermal Conductivity ◽  
Inverse Problem ◽  
Approximate Solution ◽  
Heat Conduction ◽  
Direct Problem ◽  
Heat Conduction Equation ◽  
Thermal Conductivity Coefficient ◽  
Conduction Equation ◽  
Liouville Fractional Derivative ◽  
Fractional Heat Conduction

In this paper an inverse problem for the space fractional heat conduction equation is investigated. Firstly, we describe the approximate solution of the direct problem. Secondly, for the inverse problem part, we define the functional illustrating the error of approximate solution. To recover the thermal conductivity coefficient we need to minimize this functional. In order to minimize this functional the Real Ant Colony Optimization (RealACO) algorithm is used. In the model we apply the Riemann-Liouville fractional derivative. The paper presents also some examples to illustrate the accuracy and stability of the presented algorithm.

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