时间-分数阶扩散方程同时反演的分数阶landweber迭代法

IF 1 4区数学 Q3 MATHEMATICS, APPLIED Journal of Applied Analysis and Computation Pub Date : 2023-01-01 DOI:10.11948/20230051

Jin Wen, Chong-Wang Yue, Zhuan-Xia Liu, Donal O'Regan

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引用次数: 0

摘要

本文研究了一类时间分数扩散方程的源项和初值的同时识别问题。该反问题是病态的，我们利用解耦的思想将其转化为基于傅里叶方法的两个算子方程。为了解决反问题，提出了分数阶Landweber正则化方法。此外，我们利用先验和后验参数选择规则给出了精确解和正则解之间的收敛估计。为了验证所提方法的准确性和有效性，构造了几个数值算例。

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A FRACTIONAL LANDWEBER ITERATION METHOD FOR SIMULTANEOUS INVERSION IN A TIME-FRACTIONAL DIFFUSION EQUATION

In the present paper, we study the problem to identify the space-dependent source term and initial value simultaneously for a time-fractional diffusion equation. This inverse problem is ill-posed, and we use the idea of decoupling to turn it into two operator equations based on the Fourier method. To solve the inverse problem, a fractional Landweber regularization method is proposed. Furthermore, we present convergence estimates between the exact solution and the regularized solution by using the a-priori and the a-posteriori parameter choice rules. In order to verify the accuracy and efficiency of the proposed method, several numerical examples are constructed.

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来源期刊

Journal of Applied Analysis and Computation MATHEMATICS, APPLIED-

CiteScore

2.30

自引率

9.10%

发文量

期刊介绍： The Journal of Applied Analysis and Computation (JAAC) is aimed to publish original research papers and survey articles on the theory, scientific computation and application of nonlinear analysis, differential equations and dynamical systems including interdisciplinary research topics on dynamics of mathematical models arising from major areas of science and engineering. The journal is published quarterly in February, April, June, August, October and December by Shanghai Normal University and Wilmington Scientific Publisher, and issued by Shanghai Normal University.