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

作者：Wei, Ting^*; Wang, Jungang

来源：Applied Numerical Mathematics, 2014, 78: 95-111.

DOI：10.1016/j.apnum.2013.12.002

• Inverse source problem
• Fractional diffusion equation
• Quasi-boundary value method
• Convergence analysis
• A priori parameter choice
• Morozov's discrepancy principle

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.

• 出版日期2014-4
• 单位兰州大学