Coupling RBF-based meshless method and Landweber iteration algorithm for approximating a space-dependent source term in a time fractional diffusion equation

The problem of determining a space-dependent source term in a time fractional diffusion equation is considered from the measured data at the final time. To find an approximation of the source term, a methodology involving minimization of the cost functional is applied. Also, in order to construct th...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 417; p. 114531
Main Author: Salehi Shayegan, Amir Hossein
Format: Journal Article
Language:English
Published: Elsevier B.V 01.01.2023
Subjects:
Inverse source problem
Landweber iteration algorithm
Lipschitz continuity
Meshless method
Radial basis functions
Time fractional diffusion equation
Radial basis functions
Inverse source problem
35R30
Meshless method
Time fractional diffusion equation
Landweber iteration algorithm
65M32
Lipschitz continuity
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:The problem of determining a space-dependent source term in a time fractional diffusion equation is considered from the measured data at the final time. To find an approximation of the source term, a methodology involving minimization of the cost functional is applied. Also, in order to construct the Landweber iteration algorithm, an explicit formula for the gradient of the cost functional J is given via the solution of an adjoint problem. The resulting adjoint problem is treated by a radial basis function method for spatial dimension and a finite difference scheme for the time fractional derivative followed by an iterative domain decomposition method to achieve a desired accuracy. In addition, Lipschitz continuity of the gradient of the cost functional, monotonicity and convergence of Landweber iteration algorithm are proved. At the end, a numerical example is given to show the validation of the iterative algorithm.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2022.114531