Tikhonov Regularisation Method for Simultaneous Inversion of the Source Term and Initial Data in a Time-Fractional Diffusion Equation
Year: 2015
East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 3 : pp. 273–300
Abstract
The inverse problem of identifying the time-independent source term and initial value simultaneously for a time-fractional diffusion equation is investigated. This inverse problem is reformulated into an operator equation based on the Fourier method. Under a certain smoothness assumption, conditional stability is established. A standard Tikhonov regularisation method is proposed to solve the inverse problem. Furthermore, the convergence rate is given for an a priori and a posteriori regularisation parameter choice rule, respectively. Several numerical examples, including one-dimensional and two-dimensional cases, show the efficiency of our proposed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.310315.030715a
East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 3 : pp. 273–300
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Time-fractional diffusion equation conditional stability Tikhonov regularisation Morozov discrepancy principle convergence rate.