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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   

  1. 西北师范大学数学与统计学院, 计算数学研究所, 兰州 730070
  • 收稿日期:2016-09-27 出版日期:2017-08-15 发布日期:2017-08-04
  • 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

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.

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.

AN ITERATIVE METHOD FOR AN INVERSE SOURCE PROBLEM OF A TIME-FRACTIONAL DIFFUSION EQUATION

Cheng Qiang, Xiong Xiangtuan   

  1. Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
  • Received:2016-09-27 Online:2017-08-15 Published:2017-08-04
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.
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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