基于域松弛非稳态迭代正则化方法求解时间分数阶扩散波方程空间源项辨识问题 Alternative Title Based on rrNIT method to solve the inverse space-dependent source problem for a time-fractional diffusion wave equation 冯正 Subtype 硕士 Thesis Advisor 魏婷 2021-05-22 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 理学硕士 Degree Discipline 计算数学 Keyword 时间分数阶扩散波方程 反演空间源项 域松弛非稳态迭代Tikhonov正则化方法 不适定性 唯一性与非唯一性 Abstract 本文利用一种新的迭代正则化方法——域松弛非稳态迭代Tikhonov正则化方法, 求解时间分数阶扩散波方程的空间源项辨识问题. 首先我们讨论了时间分数阶扩散波方程空间源项辨识问题的不适定性、唯一性与非唯一性, 其次我们介绍域松弛非稳态迭代Tikhonov正则化方法, 最后给出正问题与反问题的数值离散求解方法, 并结合具体的数值算例说明算法的有效性. Other Abstract In this thesis, a new iterative regularization method, called range-relaxed non-stationary iterative Tikhonov method, is used to study the identification of space-dependent source term for a time fractional diffusion wave equation. Firstly, we discuss the ill-posedness, uniqueness and non-uniqueness of the problem to identify space-dependent source term for the time fractional diffusion wave equation. Secondly, we will introduce range-relaxed non-stationary iterative Tikhonov method. Finally, we will give the numerical methods of direct problem and inverse problem. Numerical experiments are given to illustrate the effectiveness of the algorithm. Pages 39 URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/459973 Collection 数学与统计学院 Affiliation 数学与统计学院 First Author Affilication School of Mathematics and Statistics Recommended CitationGB/T 7714 冯正. 基于域松弛非稳态迭代正则化方法求解时间分数阶扩散波方程空间源项辨识问题[D]. 兰州. 兰州大学,2021.
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