A modified fractional Landweber method for a backward problem for the inhomogeneous time-fractional diffusion equation in a cylinder

Abstract

In this paper, we consider a backward problem for the inhomogeneous time-fractional diffusion equation in a cylinder. Such a problem is ill-posed. Based on the solution given by the separation of variables, we apply a modified fractional Landweber method to solve it. Error estimates are presented under the a-priori and the a-posteriori choice rules for regularization parameters, respectively. Relative to the classical Landweber method, the modified fractional Landweber method can reduce the total number of iterations to achieve the same accuracy. Numerical example is given to show the validity of the scheme.

Keywords:

• Backward problem
• modified fractional Landweber method
• error estimate

AMS Subject Classifications:

• 35R25
• 35R30
• 65J20
• 65M30

Acknowledgments

We thank the referees for careful reviewing and for pointing out some nice ideas. This work is partially supported by the Natural Science Foundation of China [grant number 11661072], the Natural Science Foundation of Northwest Normal University, China [grant number NWNU-LKQN-17-5].

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China (No 11661072), the Natural Science Foundation of Northwest Normal University, China (No NWNU-LKQN-17-5).