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Afshin Babaei

Afshin Babaei

Academic rank: Associate Professor
ORCID: https://orcid.org/0000-0002-6980-9786
Education: PhD.
ScopusId: https://www.scopus.com/authid/detail.uri?authorId=57188696707
Faculty: Faculty of Mathematical Sciences
Address: Department of Mathematics, Faculty of Mathematical sciences, University of Mazandaran, Babolsar, Iran
Phone: 011-35302418

Research

Title
Numerical Method Based on the Jacobi Polynomials to Reconstruct an Unknown Source Term in a Time Fractional Diffusion-wave Equation
Type
JournalPaper
Keywords
inverse source problem, Jacobi polynomials, Caputo's fractional derivative, time fractional diffusion-wave equation, Tikhonov regularization.
Year
2019
Journal TAIWANESE JOURNAL OF MATHEMATICS
DOI
Researchers Somayeh Nemati ، Afshin Babaei

Abstract

In this paper, we consider an inverse problem of identifying an unknown time dependent source function in a time-fractional diffusion-wave equation. First, some basic properties of the shifted Jacobi polynomials (SJPs) are presented. Then, the analytical solution of the direct problem is given and used to obtain an approximation of the unknown source function in a series of SJPs. Due to ill-posedness of this inverse problem, the Tikhonov regularization method with Morozov's discrepancy principle criterion is applied to nd a stable solution. After that, an error bound is obtained for the approximation of the unknown source function. Finally, some numerical examples are provided to show e ectiveness and robustness of the proposed algorithm.