Identification of an Inverse Source Problem in a Fractional Partial Differential Equation Based on Sinc-Galerkin Method and TSVD Regularization-Reference-Cited by-同舟云学术

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

Published:2023-06-06 Issue:1 Volume:24 Page:215-237
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Safaie Ali¹,Salehi Shayegan Amir Hossein²^ORCID,Shahriari Mohammad¹

Affiliation:

1. Department of Mathematics , Faculty of Science , University of Maragheh , Maragheh , Iran

2. Mathematics Department , Faculty of Basic Science , Khatam-ol-Anbia (PBU) University , Tehran , Iran

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/cmam-2022-0178/pdf

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