Comparative Analysis of Methods for Regularizing an Initial Boundary Value Problem for the Helmholtz Equation

الملخص EN

We consider an ill-posed initial boundary value problem for the Helmholtz equation.

This problem is reduced to the inverse continuation problem for the Helmholtz equation.

We prove the well-posedness of the direct problem and obtain a stability estimate of its solution.

We solve numerically the inverse problem using the Tikhonov regularization, Godunov approach, and the Landweber iteration.

Comparative analysis of these methods is presented.