解一类时间分数阶逆扩散问题的 Landweber 迭代法

数学物理学报 ›› 2026, Vol. 46 ›› Issue (1): 80-93.

解一类时间分数阶逆扩散问题的 Landweber 迭代法

刘云泽, 冯立新^*()

黑龙江大学数学科学学院哈尔滨 150080

收稿日期:2024-10-21 修回日期:2025-09-17 出版日期:2026-02-26 发布日期:2026-01-19
通讯作者: 冯立新 E-mail:fenglixin@hlju.edu.cn
基金资助:
国家自然科学基金(12101205);黑龙江省自然科学基金(PL2024A010)

Landweber Iterative Method for a Time Fractional Inverse Diffusion Problem

Yunze Liu, Lixin Feng^*()

School of Mathematical Science, Heilongjiang University, Harbin 150080

Received:2024-10-21 Revised:2025-09-17 Online:2026-02-26 Published:2026-01-19
Contact: Lixin Feng E-mail:fenglixin@hlju.edu.cn
Supported by:
NSFC(12101205);Natural Science Foundation of Heilongjiang Province of China(PL2024A010)

摘要/Abstract

摘要：

该文研究一类时间 Caputo 分数阶逆扩散问题. 文中应用 Landweber 迭代法解这一不适定问题分别给出了先验条件和后验条件下迭代次数 (正则化参数) 的选取准则, 并且给出了该方法收敛性的严格数学证明. 最后数值实验表明了Landweber 迭代方法解该问题的有效性.

关键词: 分数阶逆扩散问题, Landweber 迭代法, 先验和后验迭代选取规则, 误差估计

Abstract:

In this paper, an inverse diffusion problem with the Caputo fractional derivative in time is considered. We prove that such a problem is ill-posed and apply the Landweber iteration method. The selection criteria for the number of iterations (regularization parameter) under both prior and posterior conditions are provided respectively, along with a rigorous mathematical proof of the convergence of the method. Finally, a numerical example is given to illustrate the effectiveness of this method.

Key words: fractional inverse diffusion problem, Landweber iterative method, a priori and a posteriori iteration choice rules, error estimate

中图分类号:

O175

刘云泽, 冯立新. 解一类时间分数阶逆扩散问题的 Landweber 迭代法[J]. 数学物理学报, 2026, 46(1): 80-93.

Yunze Liu, Lixin Feng. Landweber Iterative Method for a Time Fractional Inverse Diffusion Problem[J]. Acta mathematica scientia,Series A, 2026, 46(1): 80-93.

图/表 3

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