A numerical method for reconstructing the potential in fractional Calderón problem with a single measurement

被引：0
|
作者：
Li, Xinyan [1 ,2 ]
机构：
[1] Shandong Univ, Res Ctr Math & Interdisciplinary Sci, Qingdao 266237, Shandong, Peoples R China
[2] Shandong Univ, Frontiers Sci Ctr Nonlinear Expectat, Minist Educ, Qingdao 266237, Shandong, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2025年 / 183卷
关键词：
Fractional Calder & oacute; n problem; Fractional Laplacian; Conjugate gradient method; Inverse problem; Tikhonov regularization; CALDERON PROBLEM; SOURCE-TERM; EQUATION; LAPLACIAN; UNIQUENESS;
D O I：
10.1016/j.camwa.2025.02.018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we develop a numerical method for determining the potential in one and two dimensional fractional Calder & oacute;n problems with a single measurement. Finite difference scheme is employed to discretize the fractional Laplacian, and the parameter reconstruction is formulated into a variational problem based on Tikhonov regularization to obtain a stable and accurate solution. Conjugate gradient method is utilized to solve the variational problem. Moreover, we also provide a suggestion to choose the regularization parameter. Numerical experiments are performed to illustrate the efficiency and effectiveness of the developed method and verify the theoretical results.
引用
收藏
页码：256 / 270
页数：15
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