The truncation method for identifying an unknown source in the Poisson equation

This paper deals with the problem of determining an unknown source which depends only on one variable in two-dimensional Poisson equation, with the aid of an extra measurement at an internal point. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. We obtain the regularization solution by the truncation method. For the regularization solution, the Hölder type stability estimate between the regularization solution and the exact solution is given. Numerical results are presented to illustrate the accuracy and efficiency of this method.