Landweber Iterative Method for an Inverse Source Problem of Time-Space Fractional Diffusion-Wave Equation

IF 1 4区 数学 Q3 MATHEMATICS, APPLIED Computational Methods in Applied Mathematics Pub Date : 2023-06-15 DOI:10.1515/cmam-2022-0240
Fan Yang, Yan Zhang, Xiao-Xiao Li
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引用次数: 0

Abstract

Abstract In this paper, we apply a Landweber iterative regularization method to determine a space-dependent source for a time-space fractional diffusion-wave equation from the final measurement. In general, this problem is ill-posed, and a Landweber iterative regularization method is used to obtain the regularization solution. Under the a priori parameter choice rule and the a posteriori parameter choice rule, we give the error estimates between the regularization solution and the exact solution, respectively. Some numerical results in the one-dimensional and two-dimensional cases show the utility of the used regularization method.
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一类时空分数阶扩散波方程反源问题的Landweber迭代方法
摘要在本文中,我们应用Landweber迭代正则化方法从最终测量中确定时空分数阶扩散波方程的空间相关源。一般来说,这个问题是不适定的,并且使用Landweber迭代正则化方法来获得正则化解。在先验参数选择规则和后验参数选择规则下,我们分别给出了正则化解和精确解之间的误差估计。一维和二维情况下的一些数值结果表明了所使用的正则化方法的实用性。
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来源期刊
CiteScore
2.40
自引率
7.70%
发文量
54
期刊介绍: The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.
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