兰州理工大学学报2024,Vol.50Issue(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

The Quasi-boundary regularization method for inverting the left boundary of fractional Schr?dinger equation

高银霞 杨帆 张成
兰州理工大学学报2024,Vol.50Issue(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

The Quasi-boundary regularization method for inverting the left boundary of fractional Schr?dinger equation

高银霞 1杨帆 1张成1
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作者信息

  • 1. 兰州理工大学理学院,甘肃兰州 730050
  • 折叠

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.

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 de-pends on the measurement data.A quasi-boundary regularization method is used to solve this inverse prob-lem,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.

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

Key words

time-fractional Schrödinger equation/inverting the left boundary/ill-posed problem/quasi-boundary regularization method

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基金项目

国家自然科学基金(11961044)

出版年

2024
兰州理工大学学报
兰州理工大学

兰州理工大学学报

CSTPCD北大核心
影响因子:0.57
ISSN:1673-5196
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