| 带有Riemann-Liouville导数的分数阶热传导方程逆源问题的正则化方法 |
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| 引用本文： | 史暖峰,冯立新. 带有Riemann-Liouville导数的分数阶热传导方程逆源问题的正则化方法[J]. 吉林大学学报(理学版), 2021, 59(4): 743-752. DOI: 10.13413/j.cnki.jdxblxb.2020403 |
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| 作者姓名： | 史暖峰 冯立新 |
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| 作者单位： | 1. 黑龙江大学 数学科学学院, 哈尔滨 150080；2. 利沃夫国立理工大学 应用数学与基础科学学院, 乌克兰 利沃夫 79013 |
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| 摘 要： | 首先,用Tikhonov正则化方法求解带有Riemann-Liouville导数的分数阶热传导方程逆源问题,得到了包含Mittag-Leffler函数的正则解;其次,对正则解进行收敛性分析,给出先验参数选取下正则解和精确解的误差估计及后验参数选取下正则化参数的取值范围.数值实验结果表明了该正则化方法的有效性.
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| 关 键 词： | 分数阶热传导方程 逆源问题 Mittag-Leffler函数 正则化方法 误差估计 |
| 收稿时间： | 2020-12-02 |
Regularization Method for Inverse Source Problem of Fractional Heat Conduction Equation with Riemann-Liouville Derivative |
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| SHI Nuanfeng,FENG Lixin. Regularization Method for Inverse Source Problem of Fractional Heat Conduction Equation with Riemann-Liouville Derivative[J]. Journal of Jilin University: Sci Ed, 2021, 59(4): 743-752. DOI: 10.13413/j.cnki.jdxblxb.2020403 |
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| Authors: | SHI Nuanfeng FENG Lixin |
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| Affiliation: | 1. College of Mathematical Sciences, Heilongjiang University, Harbin 150080, China;
2. College of Applied Mathematics and Basic Science, Lviv Polytechnic National University, Lviv 79013, Ukraine
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| Abstract: | Firstly, by using Tikhonov regularization method to solve the inverse source problem of the fractional heat conduction equation with Riemann-Liouville derivative, we obtained a regularization solution with Mittag-Leffler function. Secondly, we analyzed the convergence of the regularization solution, gave the error estimate of the regularization and exact solutions under a priori parameter choice rule, and the range of regularization parameter under a posterior parameter choice rule. The numerical experiment results show the effectiveness of proposed regularization method. |
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| Keywords: | fractional heat conduction equation inverse source problem Mittag-Leffler function regularization method error estimate |
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