Numerical inversion of reaction parameter for a time-fractional diffusion equation by Legendre spectral collocation and mollification method

In this paper, we consider an inverse problem of identifying a pair of function {u(x,t),r(t)} in the time fractional diffusion equation from two kinds of observations. By virtue of the high-precision Legendre spectral collocation and mollification method in the spatial and time direction severally,...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2022-12, Vol.128, p.188-197
Main Authors: Zhang, Wen, Ding, Zirong, Wang, Zewen, Ruan, Zhousheng
Format: Article
Language:English
Subjects:
Dirichlet boundary condition
Inverse problem
Legendre collocation method
Mollification method
Time fractional derivative
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Summary:In this paper, we consider an inverse problem of identifying a pair of function {u(x,t),r(t)} in the time fractional diffusion equation from two kinds of observations. By virtue of the high-precision Legendre spectral collocation and mollification method in the spatial and time direction severally, we present an efficient algorithm to solve the inverse problem. Finally, two numerical examples explicate the effectiveness and stability of the proposed method.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2022.10.022