Spectral regularization method for solving a time-fractional inverse diffusion problem
作者:
Highlights:
•
摘要
In this paper, we consider an inverse problem for a time-fractional diffusion equation with one-dimensional semi-infinite domain. The temperature and heat flux are sought from a measured temperature history at a fixed location inside the body. We show that such problem is severely ill-posed and further apply a spectral regularization method to solve it based on the solution given by the Fourier method. Convergence estimates are presented under a priori bound assumptions for the exact solution. Finally, numerical examples are given to show that the proposed numerical method is effective.
论文关键词:Spectral regularization,Time-fractional inverse diffusion,Caputo’s fractional derivatives,Temperature,Heat flux,Fourier transform,Laplace transform
论文评审过程:Available online 21 June 2011.
论文官网地址:https://doi.org/10.1016/j.amc.2011.05.076