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A potential‐free field inverse time‐fractional Schrödinger problem: Optimal error bound analysis and regularization method
Author(s) -
Yang Fan,
Fu JunLiang,
Li XiaoXiao
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6826
Subject(s) - mathematics , regularization (linguistics) , a priori and a posteriori , inverse problem , backus–gilbert method , upper and lower bounds , inverse , convergence (economics) , regularization perspectives on support vector machines , mathematical optimization , mathematical analysis , tikhonov regularization , computer science , philosophy , geometry , epistemology , economics , economic growth , artificial intelligence
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.