Identification of an Inverse Source Problem in a Fractional Partial Differential Equation Based on Sinc-Galerkin Method and TSVD Regularization

In this paper, using Sinc-Galerkin method and TSVD regularization, an approximation of the quasi-solution to an inverse source problem is obtained. To do so, the solution of direct problem is obtained by the Sinc-Galerkin method, and this solution is applied in a least squares cost functional. Then,...

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Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 24; no. 1; pp. 215 - 237
Main Authors Safaie, Ali, Salehi Shayegan, Amir Hossein, Shahriari, Mohammad
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.01.2024
Walter de Gruyter GmbH
Subjects
35R30
65F22
Approximation
Error analysis
Fractional Partial Differential Equation
Galerkin method
Inverse Source Problem
Mathematics
Partial differential equations
Quasi-solution
Regularization
Sinc-Galerkin Method
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Summary:In this paper, using Sinc-Galerkin method and TSVD regularization, an approximation of the quasi-solution to an inverse source problem is obtained. To do so, the solution of direct problem is obtained by the Sinc-Galerkin method, and this solution is applied in a least squares cost functional. Then, to obtain an approximation of the quasi-solution, we minimize the cost functional by TSVD regularization. Error analysis and convergence of the proposed method are investigated. In addition, at the end, four numerical examples are given in details to show the efficiency and accuracy of the proposed method.
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ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2022-0178