A Posteriori Regularization Parameter Choice Rule for Truncation Method for Identifying the Unknown Source of the Poisson Equation

الملخص EN

We consider the problem of determining an unknown source which depends only on one variable in two-dimensional Poisson equation.

We prove a conditional stability for this problem.

Moreover, we propose a truncation regularization method combined with an a posteriori regularization parameter choice rule to deal with this problem and give the corresponding convergence estimate.

Numerical results are presented to illustrate the accuracy and efficiency of this method.