Math. Model. Nat. Phenom.
Volume 13, Number 1, 2018
Theory and applications of fractional differentiation
|Number of page(s)||14|
|Published online||06 April 2018|
Reconstruction of the Robin boundary condition and order of derivative in time fractional heat conduction equation
Institute of Mathematics, Silesian University of Technology,
* Corresponding author: firstname.lastname@example.org
Accepted: 3 October 2017
This paper describes an algorithm for reconstruction the boundary condition and order of derivative for the heat conduction equation of fractional order. This fractional order derivative was applied to time variable and was defined as the Caputo derivative. The heat transfer coefficient, occurring in the boundary condition of the third kind, was reconstructed. Additional information for the considered inverse problem is given by the temperature measurements at selected points of the domain. The direct problem was solved by using the implicit finite difference method. To minimize functional defining the error of approximate solution an Artificial Bee Colony (ABC) algorithm and Nelder-Mead method were used. In order to stabilize the procedure the Tikhonov regularization was applied. The paper presents examples to illustrate the accuracy and stability of the presented algorithm.
Mathematics Subject Classification: 35Q53 / 34B20 / 35G31
Key words: Inverse problem / Caputo derivative / fractional heat conduction equation
© EDP Sciences, 2018
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