计算数学
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计算数学  2017, Vol. 39 Issue (3): 295-308    DOI:
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时间分数次扩散方程反演源项问题的迭代正则化方法
程强, 熊向团
西北师范大学数学与统计学院, 计算数学研究所, 兰州 730070
AN ITERATIVE METHOD FOR AN INVERSE SOURCE PROBLEM OF A TIME-FRACTIONAL DIFFUSION EQUATION
Cheng Qiang, Xiong Xiangtuan
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
 全文: PDF (389 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 时间分数次扩散方程中反演源项问题是一类经典不适定问题.本文构造了一种新的迭代格式作为正则化方法,给出了先验和后验参数选取下相应的收敛性分析.数值算例验证该方法的有效性.
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关键词时间分数阶扩散方程   迭代正则化方法   先验参数选取   后验参数选取   误差估计     
Abstract: Inverse source problems for time-fractional diffusion equation is a classical ill-posed inverse problem. A new iterative scheme is devised for solving this problem. Under the a-priori and post-priori parameter choice rules, the convergence rates are obtained. Some numerical tests are conducted for showing the effectiveness of the proposed method.
Key wordsTime-fractional diffusion equation   iterative regularization   a-priori choice rule   post-priori choice rule   error estimate   
收稿日期: 2016-09-27;
基金资助:

国家自然科学基金(11661072)和西北师范大学博士启动金(5002-577)资助项目

引用本文:   
. 时间分数次扩散方程反演源项问题的迭代正则化方法[J]. 计算数学, 2017, 39(3): 295-308.
. AN ITERATIVE METHOD FOR AN INVERSE SOURCE PROBLEM OF A TIME-FRACTIONAL DIFFUSION EQUATION[J]. Mathematica Numerica Sinica, 2017, 39(3): 295-308.
 
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