Tikhonov type regularization method for the Cauchy problem of the modified Helmholtz equation

摘要

In this paper, we propose a numerical method for solving the Cauchy problem of the modified Helmholtz equation. By using Green’s formula, the Cauchy problem is transformed to a moment problem. Then we propose a Tikhonov type regularization algorithm for obtaining an approximate solution to the Neumann date on the unspecified boundary. Convergence analysis and error estimation are also discussed. For numerical verification, several numerical examples in the two-dimensional case are presented.