[1]邱淑芳,王泽文,曾祥龙,等.一类时间分数阶扩散方程中的源项反演解法[J].江西师范大学学报(自然科学版),2018,(06):610-615.[doi:10.16357/j.cnki.issn1000-5862.2018.06.11]
　QIU Shufang,WANG Zewen,ZENG Xianglong,et al.The Numerical Method for Reconstructing Source Term in a Time Fractional Diffusion Equation[J].Journal of Jiangxi Normal University:Natural Science Edition,2018,(06):610-615.[doi:10.16357/j.cnki.issn1000-5862.2018.06.11]
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一类时间分数阶扩散方程中的源项反演解法()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2018年06期
页码:
610-615
栏目:
数学与应用数学
出版日期:
2018-12-20

文章信息/Info

Title:
The Numerical Method for Reconstructing Source Term in a Time Fractional Diffusion Equation
文章编号:
1000-5862(2018)06-0610-06
作者:
邱淑芳; 王泽文; 曾祥龙; 胡 彬
东华理工大学理学院,江西 南昌 330013
Author(s):
QIU Shufang; WANG Zewen; ZENG Xianglong; HU Bin
School of Science,East China University of Technology,Nanchang Jiangxi 330013,China
关键词:
不适定问题;  时间分数阶方程;  源项反演;  正则化方法;  磨光方法
Keywords:
ill-posed problem;  time fractional equation;  source inversion;  regularization method;  mollification method
分类号:
O 175.8
DOI:
10.16357/j.cnki.issn1000-5862.2018.06.11
文献标志码:
A
摘要:
考虑了一类具有Neumann边界的时间分数阶扩散方程源项反演问题.首先,从分离变量法出发将反问题归结为第1类Volterra积分方程,从而揭示出反问题的不适定性; 其次,为了获得反问题的条件稳定性,通过分数阶数值微分将第1类Volterra积分方程转化为第2类Volterra积分方程,建立源项反问题的条件稳定性和误差估计; 最后,引进磨光正则化,获得稳定的分数阶数值导数,将其代入求解第2类积分方程,从而稳定地重建出仅依赖时间变量的源项.数值实验结果验证了所得反演算法的有效性.
Abstract:
An inverse source problem in a time fractional diffusion equation with Neumann boundary is considered.Firstly,from the method of separation of variables for solving the direct problem,the inverse source problem is turned into a Volterra integral equation of the first kind,which reveals ill-posedness of the inverse problem.Secondly,for obtaining conditional stability of the inverse problem,the Volterra integral equation of the first kind is transformed into a second kind Volterra integral equation by using fractional derivative,then the conditional stability and error estimate are established.Lastly,from stable approximation of the fractional derivative computed by utilizing the mollification regularization,the time-dependent source term is reconstructed stably by solving the Volterra integral equation of the second kind.Results of numerical experiments verify the effectiveness of the inversion algorithm.

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备注/Memo

备注/Memo:
收稿日期:2018-06-20
基金项目:国家自然科学基金(11761007,11561003),江西省主要学科学术与技术带头人计划(20172BCB22019),江西省高校科技落地计划(KJLD14051)和江西省教育厅科技课题(GJJ170473)资助项目.
通信作者:邱淑芳(1972-),女,江西南昌人,副教授,主要从事数学建模与反问题的数值解法研究.E-mail:shfqiu@ecit.cn
更新日期/Last Update: 2018-12-20