A potential‐free field inverse time‐fractional Schrödinger problem: Optimal error bound analysis and regularization method

Abstract

In this paper, an inverse time-fractional Schrödinger problem of potential-free field is studied. This problem is ill-posed; that is, 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 a priori regularization parameter selection rule is optimal, and the convergence error estimate obtained under the a posteriori regularization parameter selection rule is order-optimal. Finally, some numerical examples are given to illustrate the effectiveness and stability of this method. KEYWORDS a modified kernel method, ill-posed problem, inverse problem, optimal error bound, time-fractional Schrödinger equation MSC CLASSIFICATION