A Fractional Tikhonov Regularisation Method for Finding Source Terms in a Time-Fractional Radial Heat Equation

A Fractional Tikhonov Regularisation Method for Finding Source Terms in a Time-Fractional Radial Heat Equation

Year:    2019

East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.090918.030119

East Asian Journal on Applied Mathematics, Vol. 9 (2019), Iss. 2 : pp. 386–408

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Inverse source problem fractional Tikhonov regularisation method error estimate.