A comparison of regularization methods for identifying unknown source problem for the modified Helmholtz equation

In this paper, three regularization methods, such as the mollification method, the modified Tikhonov regularization method, the Fourier regularization method, for the identification of an unknown source for the modified Helmholtz equation are considered and compared. We have solved the model problem with these methods, investigated the differences between them, analyzed their convergence estimates under a priori choice of the regularization parameter and proved the effectiveness of these methods. Two numerical examples are provided to show the main results.