Numerical Solution to the Space-Time Fractional Diffusion Equation and Inversion for the Space-Dependent Diffusion Coefficient

作者：Chi, Guangsheng; Li, Gongsheng^*; Sun, Chunlong; Jia, Xianzheng

来源：Journal of Computational and Theoretical Transport, 2017, 46(2): 122-146.

DOI：10.1080/23324309.2016.1263667

• Anomalous diffusion
• convergence and stability
• homotopy regularization algorithm
• inverse problem
• numerical inversion
• Space-time fractional derivatives

This paper deals with numerical solution for the space-time fractional diffusion equation with variable diffusion coefficient, and numerical inversion for the space-dependent diffusion coefficient by the homotopy regularization algorithm. An equivalent system to the forward problem is deduced by utilizing properties of the fractional derivatives, and an implicit finite difference scheme for solving the forward problem is set forth, and its stability and convergence are proved based on estimation to the spectrum radius of the coefficient matrix. The homotopy regularization algorithm is introduced to solve the inverse problem, and numerical inversions are performed with noisy data. The inversion solutions give good approximations to the exact solution as the noise level goes to small demonstrating a numerical stability of the inverse problem here.

• 出版日期2017
• 单位山东理工大学; 山东大学; 东南大学