@Article{EAJAM-5-273,
author = {Zhousheng Ruan, Jerry Zhijian Yang and Xiliang Lu},
title = {Tikhonov Regularisation Method for Simultaneous Inversion of the Source Term and Initial Data in a Time-Fractional Diffusion Equation},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {5},
number = {3},
pages = {273--300},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.310315.030715a},
url = {http://global-sci.org/intro/article_detail/eajam/10810.html}
}