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

• Published in: Mathematical modelling and analysis Vol. 29; no. 1; pp. 23 - 45
• Main Authors: Djemoui, Sebti, Meziani, Mohamed S. E., Boussetila, Nadjib
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 22.02.2024
• Subjects: a posteriori parameter choice rule; Algorithms; Analysis; Boundary conditions; Boundary value problems; Exact solutions; fractional elliptic equations; Functions, Elliptic; ill-posed problems; Inverse problems; Iterative methods; Iterative methods (Mathematics); iterative regularization method; Partial differential equations; Regularization; Regularization methods; Stability; Tests, problems and exercises; Tricomi-Gellerstedt-Keldysh equations; France; fractional elliptic equations; ill-posed problems; Tricomi-Gellerstedt-Keldysh equations; a posteriori parameter choice rule; iterative regularization method; inverse problems
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2024.16783

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.