分数阶薛定谔方程反演左边界的拟边界正则化方法

兰州理工大学学报 ›› 2024, Vol. 50 ›› Issue (4): 147-152.

分数阶薛定谔方程反演左边界的拟边界正则化方法

高银霞, 杨帆^*, 张成

兰州理工大学理学院, 甘肃兰州 730050

收稿日期:2022-09-01 出版日期:2024-08-28 发布日期:2024-08-30
通讯作者: 杨帆(1976-),男,甘肃灵台人,博士,教授.Email:yfggd114@163.com
基金资助:
国家自然科学基金(11961044)

The Quasi-boundary regularization method for inverting the left boundary of fractional Schrödinger equation

GAO Yin-xia, YANG Fan, ZHANG Cheng

School of Science, Lanzhou Univ. of Tech., Lanzhou 730050, China

Received:2022-09-01 Online:2024-08-28 Published:2024-08-30

摘要/Abstract

摘要： 研究无界区域上时间分数阶薛定谔方程的反演左边界反问题,这是一个不适定问题,即问题的解不连续依赖于测量数据.利用拟边界正则化方法求解此反问题,给出拟边界正则解.在先验和后验正则化参数选取规则之下给出正则解和精确解的误差估计.

关键词: 时间分数阶薛定谔方程, 反演左边界, 不适定问题, 拟边界正则化方法

Abstract: The problem of inverting the left boundary of the time-fractional Schrödinger equation in the unbounded region is studied, which is an ill-posed problem, meaning that the solution discontinuously depends on the measurement data. A quasi-boundary regularization method is used to solve this inverse problem, and its regularized solution is given. The error estimates between the regularization solution and the exact solution are derived under the priori and the posteriori regularization parameter selection rule.

Key words: time-fractional Schrödinger equation, inverting the left boundary, ill-posed problem, quasi-boundary regularization method.

中图分类号:

O175

高银霞, 杨帆, 张成. 分数阶薛定谔方程反演左边界的拟边界正则化方法[J]. 兰州理工大学学报, 2024, 50(4): 147-152.

GAO Yin-xia, YANG Fan, ZHANG Cheng. The Quasi-boundary regularization method for inverting the left boundary of fractional Schrödinger equation[J]. Journal of Lanzhou University of Technology, 2024, 50(4): 147-152.

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