Volume 9, Issue 2
A Fractional Tikhonov Regularisation Method for Finding Source Terms in a Time-Fractional Radial Heat Equation

Shuping Yang & Xiangtuan Xiong

East Asian J. Appl. Math., 9 (2019), pp. 386-408.

Published online: 2019-03

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  • Abstract

The ill-posed problems of the identification of unknown source terms in a time-fractional radial heat conduction problem are studied. To overcome the difficulties caused by the ill-posedness, a fractional Tikhonov regularisation method is proposed. Employing Mittag-Leffler function, we obtain error estimates under a priori and a posteriori regularisation parameter choices. In the last situation, the Morozov discrepancy principle is also used. Numerical examples show that the method is a stable and effective tool in the reconstruction of smooth and non-smooth source terms and, generally, outperforms the classical Tikhonov regularisation.

  • Keywords

Inverse source problem, fractional Tikhonov regularisation method, error estimate.

  • AMS Subject Headings

35R25, 35R30, 65J20, 65M30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-386, author = {}, title = {A Fractional Tikhonov Regularisation Method for Finding Source Terms in a Time-Fractional Radial Heat Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {2}, pages = {386--408}, abstract = {

The ill-posed problems of the identification of unknown source terms in a time-fractional radial heat conduction problem are studied. To overcome the difficulties caused by the ill-posedness, a fractional Tikhonov regularisation method is proposed. Employing Mittag-Leffler function, we obtain error estimates under a priori and a posteriori regularisation parameter choices. In the last situation, the Morozov discrepancy principle is also used. Numerical examples show that the method is a stable and effective tool in the reconstruction of smooth and non-smooth source terms and, generally, outperforms the classical Tikhonov regularisation.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.090918.030119 }, url = {http://global-sci.org/intro/article_detail/eajam/13089.html} }
TY - JOUR T1 - A Fractional Tikhonov Regularisation Method for Finding Source Terms in a Time-Fractional Radial Heat Equation JO - East Asian Journal on Applied Mathematics VL - 2 SP - 386 EP - 408 PY - 2019 DA - 2019/03 SN - 9 DO - http://doi.org/10.4208/eajam.090918.030119 UR - https://global-sci.org/intro/article_detail/eajam/13089.html KW - Inverse source problem, fractional Tikhonov regularisation method, error estimate. AB -

The ill-posed problems of the identification of unknown source terms in a time-fractional radial heat conduction problem are studied. To overcome the difficulties caused by the ill-posedness, a fractional Tikhonov regularisation method is proposed. Employing Mittag-Leffler function, we obtain error estimates under a priori and a posteriori regularisation parameter choices. In the last situation, the Morozov discrepancy principle is also used. Numerical examples show that the method is a stable and effective tool in the reconstruction of smooth and non-smooth source terms and, generally, outperforms the classical Tikhonov regularisation.

Shuping Yang & Xiangtuan Xiong. (2019). A Fractional Tikhonov Regularisation Method for Finding Source Terms in a Time-Fractional Radial Heat Equation. East Asian Journal on Applied Mathematics. 9 (2). 386-408. doi:10.4208/eajam.090918.030119
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