| 时间分数次扩散方程反演源项问题的迭代正则化方法 |
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| 引用本文： | 程强,熊向团. 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 |
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| 作者姓名： | 程强 熊向团 |
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| 作者单位： | 西北师范大学数学与统计学院, 计算数学研究所, 兰州 730070 |
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| 基金项目： | 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 |
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| 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 |
AN ITERATIVE METHOD FOR AN INVERSE SOURCE PROBLEM OF A TIME-FRACTIONAL DIFFUSION EQUATION |
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| Cheng Qiang,Xiong Xiangtuan. 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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| Authors: | Cheng Qiang Xiong Xiangtuan |
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| Affiliation: | Department of Mathematics, Northwest Normal University, Lanzhou 730070, China |
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| 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. |
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| Keywords: | Time-fractional diffusion equation iterative regularization a-priori choice rule post-priori choice rule error estimate |
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