A numerical method for solving retrospective inverse problem of fractional parabolic equation

被引：4
作者：
Su, Lingde [1 ,4 ]
Huang, Jian [2 ,3 ]
Vasil'ev, V. I. [4 ]
Li, Ao [2 ,3 ]
Kardashevsky, A. M. [4 ]
机构：
[1] Zaozhuang Univ, Sch Math & Stat, Zaozhuang, Shandong, Peoples R China
[2] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan, Peoples R China
[3] Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan, Peoples R China
[4] North Eastern Fed Univ, Inst Math & Informat Sci, Yakutsk, Republic Of Sak, Russia
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 413卷
基金：
中国国家自然科学基金; 俄罗斯科学基金会;
关键词：
Time fractional parabolic equation; Inverse problem; Caputo fractional derivatives; Ill-posed problems; Conjugate gradients method; SAVITZKY-GOLAY; HEAT-LIKE; DIFFUSION; APPROXIMATE; COEFFICIENT;
D O I：
10.1016/j.cam.2022.114366
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An effective numerical method for solving the inverse problem of time fractional parabolic equation is constructed in this paper. We use implicit finite difference method to discretize the problem and for the inverse problem we propose a conjugate gradient type regularization method to solve the discretized ill-posed linear systems. By comparing the different errors and the results with different perturbed data in several numerical experiments, our method is shown to solve the inverse problem, even with some noisy measurements, efficiently and stably. (c) 2022 Elsevier B.V. All rights reserved.
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页数：11
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