A modified quasi-boundary value method for an inverse source problem of the time-fractional diffusion equation

Authors:
Ting Wei;Jungang Wang
Affiliations:
-;-
Venue:
Applied Numerical Mathematics
Year:
2014

Citing 13
Cited 0

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
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High-order finite element methods for time-fractional partial differential equations

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A new regularization method for a Cauchy problem of the time fractional diffusion equation

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Two regularization methods to identify a space-dependent source for the time-fractional diffusion equation

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Abstract

In this paper, we consider an inverse source problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain. That is to determine a space-dependent source term in the time-fractional diffusion equation from a noisy final data. Based on a series expression of the solution, we can transform the original inverse problem into a first kind integral equation. The uniqueness and a conditional stability for the space-dependent source term can be obtained. Further, we propose a modified quasi-boundary value regularization method to deal with the inverse source problem and obtain two kinds of convergence rates by using an a priori and an a posteriori regularization parameter choice rule, respectively. Numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed method.