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

Abstract

This paper considers the inverse problem of determining an unknown source which depends only one spatial variable on modified Helmholtz equation. This problem is well known to be severely ill-posed, the solution (if it exists) does not depend continuously on the data. Landweber iterative regularization method is used to solve this inverse source problem. The Hölder type error estimates are obtained between the exact solution and regularization solutions under an a priori and an a posteriori regularization parameters choice rules, respectively. Numerical examples are provided to show the effectiveness of the proposed method.

Keywords

• modified helmholtz equation
• ill-posed problem
• posteriori regularization parameter choice rule
• landweber iterative method