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A coupled method for inverse source problem of spatial fractional anomalous diffusion equations. (English) Zbl 1204.65116

Summary: Based on the best perturbation method, a coupled method is developed to solve the inverse source problem of spatial fractional anomalous diffusion equation. The ill-posed inverse problem is first transformed into a well-posed problem by a Tikhonov regularization algorithm. Then the corresponding direct problem is solved by the implicit difference method, in which the source term is estimated by the best perturbation method. The efficiency and the accuracy of the proposed method are demonstrated by two numerical examples.

MSC:

65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R11 Fractional partial differential equations
65R30 Numerical methods for ill-posed problems for integral equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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