Taiwanese Journal of Mathematics

A Numerical Method Based on the Jacobi Polynomials to Reconstruct an Unknown Source Term in a Time Fractional Diffusion-wave Equation

Somayeh Nemati and Afshin Babaei

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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 find 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 effectiveness and robustness of the proposed algorithm.

Article information

Source
Taiwanese J. Math., Advance publication (2019), 19 pages.

Dates
First available in Project Euclid: 2 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1546419620

Digital Object Identifier
doi:10.11650/tjm/181210

Subjects
Primary: 65M32: Inverse problems 35R11: Fractional partial differential equations 35R30: Inverse problems

Keywords
inverse source problem Jacobi polynomials Caputo's fractional derivative time fractional diffusion-wave equation Tikhonov regularization

Citation

Nemati, Somayeh; Babaei, Afshin. A Numerical Method Based on the Jacobi Polynomials to Reconstruct an Unknown Source Term in a Time Fractional Diffusion-wave Equation. Taiwanese J. Math., advance publication, 2 January 2019. doi:10.11650/tjm/181210. https://projecteuclid.org/euclid.twjm/1546419620


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