A potential-free field inverse time-fractional
Schrödinger problem: optimal error bound
analysis and regularization method
Abstract
In this paper, an inverse time-fractional
Schr$\ddot{o}$dinger problem of potential-free field
is studied. This problem is ill-posed, i.e, the solution (if it exists)
does not depend continuously on the data. Based on an a priori bound
condition, the optimal error bound analysis is given. Moreover, a
modified kernel method is introduced. The convergence error estimate
obtained by this method under the priori regularization parameter
selection rule is optimal, and the convergence error estimate obtained
under the posteriori regularization parameter selection rule is
order-optimal. Finally, some numerical examples are given to illustrate
the effectiveness and stability of this method.