The conditional stability and an iterative regularization method for a fractional inverse elliptic problem of Tricomi-Gellerstedt-Keldysh type

The present paper is devoted to identifying an inaccessible boundary condition for a fractional elliptic problem of Tricomi-Gellerstedt-Keldysh-type. Using the expansion Fourier method, the considered problem can be reformulated as an operator equation of the first kind. To construct a stabilized ap...

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Published inMathematical modelling and analysis Vol. 29; no. 1; pp. 23 - 45
Main Authors Djemoui, Sebti, Meziani, Mohamed S. E., Boussetila, Nadjib
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 22.02.2024
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ISSN1392-6292
1648-3510
1648-3510
DOI10.3846/mma.2024.16783

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Summary:The present paper is devoted to identifying an inaccessible boundary condition for a fractional elliptic problem of Tricomi-Gellerstedt-Keldysh-type. Using the expansion Fourier method, the considered problem can be reformulated as an operator equation of the first kind. To construct a stabilized approximate solution we employ a variant of the iterative method. We also present error estimates between the exact solution and the regularized solution by the a priori and the a posteriori parameter choice rules. Finally, some numerical verifications on the efficiency and accuracy of the proposed algorithm is presented.
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ISSN:1392-6292
1648-3510
1648-3510
DOI:10.3846/mma.2024.16783