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

  • Ali Safaie , Amir Hossein Salehi Shayegan ORCID logo EMAIL logo and Mohammad Shahriari

Abstract

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.

MSC 2010: 35R30; 65F22

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Received: 2022-09-05
Revised: 2023-04-23
Accepted: 2023-04-26
Published Online: 2023-06-06
Published in Print: 2024-01-01

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