A modified Tikhonov regularization method for a Cauchy problem of a time fractional diffusion equation
In this paper, we consider a Cauchy problem of the time fractional diffusion equation
(TFDE) in x ∈ [0,L]. This problem is ubiquitous in science and engineering applications. The illposedness
of the Cauchy problem is explained by its solution in frequency domain. Furthermore,
the problem is formulated into a minimization problem with a modified Tikhonov regularization
method. The gradient of the regularization functional based on an adjoint problem is deduced
and the standard conjugate gradient method is presented for solving the minimization problem.
The error estimates for the regularized solutions are obtained under Hp norm priori bound
assumptions. Finally, numerical examples illustrate the effectiveness of the proposed method.
关键词：
Cauchy problem,
time-fractional diffusion equation,
a modified Tikhonov regularization method,
conjugate gradient method,
error estimates
