TY - JOUR
T1 - Tikhonov Regularisation Method for Simultaneous Inversion of the Source Term and Initial Data in a Time-Fractional Diffusion Equation
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 273
EP - 300
PY - 2018
DA - 2018/02
SN - 5
DO - http://doi.org/10.4208/eajam.310315.030715a
UR - https://global-sci.org/intro/article_detail/eajam/10810.html
KW - Time-fractional diffusion equation, conditional stability, Tikhonov regularisation, Morozov discrepancy principle, convergence rate.
AB - <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>