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October, 2019 A Numerical Method Based on the Jacobi Polynomials to Reconstruct an Unknown Source Term in a Time Fractional Diffusion-wave Equation
Somayeh Nemati, Afshin Babaei
Taiwanese J. Math. 23(5): 1271-1289 (October, 2019). DOI: 10.11650/tjm/181210

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.

Citation

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Somayeh Nemati. Afshin Babaei. "A Numerical Method Based on the Jacobi Polynomials to Reconstruct an Unknown Source Term in a Time Fractional Diffusion-wave Equation." Taiwanese J. Math. 23 (5) 1271 - 1289, October, 2019. https://doi.org/10.11650/tjm/181210

Information

Received: 24 December 2017; Revised: 12 October 2018; Accepted: 19 December 2018; Published: October, 2019
First available in Project Euclid: 2 January 2019

zbMATH: 07126948
MathSciNet: MR4012379
Digital Object Identifier: 10.11650/tjm/181210

Subjects:
Primary: 35R11, 35R30, 65M32

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

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Vol.23 • No. 5 • October, 2019
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