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In this paper, we consider the inverse problem of identifying the unknown source for the modified Helmholtz equation. We propose the Landweber iterative regularization method to solve this problem and obtain the regularization solution. Under the a priori and a posteriori regularization parameters choice rules, we all obtain the Hölder type error estimates between the exact solution and the regularization solutions. Several numerical examples are also provided to show that the Landweber iterative method works well for solving this problem.

Landweber iterative regularization method for identifying the unknown source of the modified Helmholtz equation