THE CONDITIONAL STABILITY AND AN ITERATIVE REGULARIZATION METHOD FOR A FRACTIONAL INVERSE ELLIPTIC PROBLEM OF TRICOMI-GELLERSTEDT-KELDYSH TYPE-Reference-Cited by-同舟云学术

THE CONDITIONAL STABILITY AND AN ITERATIVE REGULARIZATION METHOD FOR A FRACTIONAL INVERSE ELLIPTIC PROBLEM OF TRICOMI-GELLERSTEDT-KELDYSH TYPE

Published:2024-02-22 Issue:1 Volume:29 Page:23-45
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
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Author:

Djemoui Sebti¹^ORCID,Meziani Mohamed S. E.²,Boussetila Nadjib³

Affiliation:

1. Higher School of industrial Technologies Annaba, P.O.Box 218, Safsaf, 23000 Annaba, Algeria

2. Department of Mathematics, ENSET Skikda, frères Bouceta, Azzaba, 21001 Skikda, Algeria

3. Department of Mathematics, University 8 Mai 1945, P.O.Box 401, 24000 Guelma, Algeria

Abstract

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.

Publisher

Vilnius Gediminas Technical University

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