@Article{EAJAM-5-273, author = {}, 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 = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.310315.030715a}, url = {http://global-sci.org/intro/article_detail/eajam/10810.html} }