基于先验估计和后验估计的改进拟边值方法在抽象分数细分模型中检测源项

IF 0.6 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Eurasian Journal of Mathematical and Computer Applications Pub Date : 2023-03-01 DOI:10.32523/2306-6172-2023-11-1-98-123
Meziani, Djemoui, Boussetila
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引用次数: 0

摘要

本文讨论了由测量的内部数据确定分数椭圆方程中未知源项的反问题。为了解决所考虑的问题,使用了一种改进的拟边值方法。应用此方法构造了正则化解。获得了精确解与其正则化近似之间的先验和后验误差估计。简要分析了所提出的正则化方法与几种标准方法之间的关系。此外,给出了一维和二维情况下的数值结果,以说明该方法的准确性和有效性。
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DETECTION OF SOURCE TERM IN AN ABSTRACT FRACTIONAL SUBDIVISION MODEL BY THE MODIFIED QUASI-BOUNDARY VALUE METHOD WITH A PRIORI AND A POSTERIORI ESTIMATE
The paper discusses the inverse problem of determining an unknown source term in a fractional elliptic equation from measured internal data. In order to solve the considered problem, a modified quasi-boundary value method is used. Applying this method a regularized solution is constructed. An a priori and a posteriori error estimates between the exact solu- tion and its regularized approximation are obtained. A brief analysis is conducted to clarify the relationship between the suggested regularization method and several standard methods. Moreover, numerical results are presented in the one-dimensional case and two-dimensional case to illustrate the accuracy and efficiency of this method.
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来源期刊
Eurasian Journal of Mathematical and Computer Applications
Eurasian Journal of Mathematical and Computer Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
1.40
自引率
0.00%
发文量
18
期刊介绍: Eurasian Journal of Mathematical and Computer Applications (EJMCA) publishes carefully selected original research papers in all areas of Applied mathematics first of all from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time Eurasian Journal of Mathematical and Computer Applications (EJMCA) will also publish survey papers. Eurasian Mathematical Journal publishes 4 issues in a year. A working language of the journal is English. Main topics are: - Mathematical methods and modeling in mechanics, mining, biology, geophysics, electrodynamics, acoustics, industry. - Inverse problems of mathematical physics: theory and computational approaches. - Medical and industry tomography. - Computer applications: distributed information systems, decision-making systems, embedded systems, information security, graphics.
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