Central difference regularization method for inverse source problem on the Poisson equation

Abstract

In this paper, we consider an inverse problem of determining an unknown source for the Poisson equation. Since this problem is mildly ill-posed, we apply a central difference regularization method to solve this problem. Furthermore, the convergence estimate is established under a priori choice of the regularization parameter. Some numerical results verify that the proposed method is stable and effective.

Keywords:

• ill-posed problem
• central difference regularization method
• unknown source
• Poisson equation

AMS Subject Classifications:

• 47A52
• 65J22

Acknowledgements

The authors wish to thank the referees for their valuable comments which helped us to improve the present paper.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11101109], [grant number 11271102]; the Natural Science Foundation of Hei-long-jiang Province of China [grant number A201107].