DETECTION OF SOURCE TERM IN AN ABSTRACT FRACTIONAL SUBDIVISION MODEL BY THE MODIFIED QUASI-BOUNDARY VALUE METHOD WITH A PRIORI AND A POSTERIORI ESTIMATE
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Abstract
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.
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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