Regularization methods for unknown source in space fractional diffusion equation

Authors:
Wenyi Tian;Can Li;Weihua Deng;Yujiang Wu
Affiliations:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China;School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China and Department of Applied Mathematics, School of Sciences, Xi'san University of Technology, Xi' ...;School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China;School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China
Venue:
Mathematics and Computers in Simulation
Year:
2012

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Abstract

We discuss determining the unknown steady source in a space fractional diffusion equation and show that both the Fourier and wavelet dual least squares regularization methods work well for the ill-posed problem. The detailed error estimates are also strictly established for both of the methods. Moreover, the algorithm implementation and the corresponding numerical results are presented for the Fourier regularization method.