**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32870

##### Identifying an Unknown Source in the Poisson Equation by a Modified Tikhonov Regularization Method

**Authors:**
Ou Xie,
Zhenyu Zhao

**Abstract:**

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.

**Keywords:**
Ill-posed problem,
Unknown source,
Poisson equation,
Tikhonov regularization method,
Discrepancy principle

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1329266

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